Isolated and Dynamical Horizons and Their Applications (original) (raw)

2004

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Abstract

Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five years a new, quasi-local framework was introduced to analyze diverse facets of black holes in

Dynamical horizons and their properties

Physical Review D, 2003

A detailed description of how black holes grow in full, non-linear general relativity is presented. The starting point is the notion of dynamical horizons. Expressions of fluxes of energy and angular momentum carried by gravitational waves across these horizons are obtained. Fluxes are local and the energy flux is positive. Change in the horizon area is related to these fluxes. A notion of angular momentum and energy is associated with cross-sections of the horizon and balance equations, analogous to those obtained by Bondi and Sachs at null infinity, are derived. These in turn lead to generalizations of the first and second laws of black hole mechanics. The relation between dynamical horizons and their asymptotic states-the isolated horizons-is discussed briefly. The framework has potential applications to numerical, mathematical, astrophysical and quantum general relativity.

PHYSICAL ASPECTS OF QUASI-LOCAL BLACK HOLE HORIZONS

We discuss some of the physical aspects expected to be associated with black holes. These include Hawking radiation, horizon entropy and cosmic censorship. In particular we focus on whether these properties are more naturally associated to causally defined horizons or quasi-local horizons.

Black holes and their horizons in semiclassical and modified theories of gravity

International Journal of Modern Physics D

For distant observers, black holes are trapped spacetime domains bounded by apparent horizons. We review properties of the near-horizon geometry emphasizing the consequences of two common implicit assumptions of semiclassical physics. The first is a consequence of the cosmic censorship conjecture, namely, that curvature scalars are finite at apparent horizons. The second is that horizons form in finite asymptotic time (i.e. according to distant observers), a property implicitly assumed in conventional descriptions of black hole formation and evaporation. Taking these as the only requirements within the semiclassical framework, we find that in spherical symmetry only two classes of dynamic solutions are admissible, both describing evaporating black holes and expanding white holes. We review their properties and present the implications. The null energy condition is violated in the vicinity of the outer horizon and satisfied in the vicinity of the inner apparent/anti-trapping horizon....

Black-hole horizons as probes of black-hole dynamics. II. Geometrical insights

Physical Review D, 2012

The understanding of strong-field dynamics near black-hole horizons is a long-standing and challenging problem in general relativity. Recent advances in numerical relativity and in the geometric characterization of blackhole horizons open new avenues into the problem. In this first paper in a series of two, we focus on the analysis of the recoil occurring in the merger of binary black holes, extending the analysis initiated in [1] with Robinson-Trautman spacetimes. More specifically, we probe spacetime dynamics through the correlation of quantities defined at the black-hole horizon and at null infinity. The geometry of these hypersurfaces responds to bulk gravitational fields acting as test screens in a scattering perspective of spacetime dynamics. Within a 3 + 1 approach we build an effective-curvature vector from the intrinsic geometry of dynamical-horizon sections and correlate its evolution with the flux of Bondi linear momentum at large distances. We employ this setup to study numerically the head-on collision of nonspinning black holes and demonstrate its validity to track the qualitative aspects of recoil dynamics at infinity. We also make contact with the suggestion that the antikick can be described in terms of a "slowness parameter" and how this can be computed from the local properties of the horizon. In a companion paper [2] we will further elaborate on the geometric aspects of this approach and on its relation with other approaches to characterize dynamical properties of black-hole horizons.

New theoretical approaches to black holes

New Astronomy Reviews, 2008

Quite recently, some new mathematical approaches to black holes have appeared in the literature. They do not rely on the classical concept of event horizon—which is very global, but on the local concept of hypersurfaces foliated by trapped surfaces. After a brief introduction to these new horizons, we focus on a viscous fluid analogy that can be developed to describe their dynamics, in a fashion similar to the membrane paradigm introduced for event horizons in the seventies, but with a significant change of sign of the bulk viscosity.

Isolated horizons in 2+12 + 12+1 gravity

Advances in Theoretical and Mathematical Physics, 2002

Using ideas employed in higher dimensional gravity, non-expanding, weakly isolated and isolated horizons are introduced and analyzed in 2+1 dimensions. While the basic definitions can be taken over directly from higher dimensions, their consequences are somewhat different because of the peculiarities associated with 2+1 dimensions. Nonetheless, as in higher dimensions, we are able to: i) analyze the horizon geometry in detail; ii) introduce the notions of mass, charge and angular momentum of isolated horizons using geometric methods; and, iii) generalize the zeroth and the first laws of black hole mechanics. The Hamiltonian methods also provide, for the first time, expressions of total angular momentum and mass of charged, rotating black holes and their relation to the analogous quantities defined at the horizon. We also construct the analog of the Newman-Penrose framework in 2+1 dimensions which should be useful in a wide variety of problems in 2+1 dimensional gravity.

Isolated Horizons: the Classical Phase Space

1999

A Hamiltonian framework is introduced to encompass non-rotating (but possibly charged) black holes that are ``isolated'' near future time-like infinity or for a finite time interval. The underlying space-times need not admit a stationary Killing field even in a neighborhood of the horizon; rather, the physical assumption is that neither matter fields nor gravitational radiation fall across the portion of the horizon under consideration. A precise notion of non-rotating isolated horizons is formulated to capture these ideas. With these boundary conditions, the gravitational action fails to be differentiable unless a boundary term is added at the horizon. The required term turns out to be precisely the Chern-Simons action for the self-dual connection. The resulting symplectic structure also acquires, in addition to the usual volume piece, a surface term which is the Chern-Simons symplectic structure. We show that these modifications affect in subtle but important ways the standard discussion of constraints, gauge and dynamics. In companion papers, this framework serves as the point of departure for quantization, a statistical mechanical calculation of black hole entropy and a derivation of laws of black hole mechanics, generalized to isolated horizons. It may also have applications in classical general relativity, particularly in the investigation of of analytic issues that arise in the numerical studies of black hole collisions.

Black holes or firewalls: A theory of horizons

Physical Review D, 2013

We present a quantum theory of black hole (and other) horizons, in which the standard assumptions of complementarity are preserved without contradicting information theoretic considerations. After the scrambling time, the quantum mechanical structure of a black hole becomes that of an eternal black hole at the microscopic level. In particular, the stretched horizon degrees of freedom and the states entangled with them can be mapped into the nearhorizon modes in the two exterior regions of an eternal black hole, whose mass is taken to be that of the evolving black hole at each moment. Salient features arising from this picture include: (i) the number of degrees of freedom needed to describe a black hole is e A/2l 2 P , where A is the area of the horizon; (ii) black hole states having smooth horizons, however, span only an e A/4l 2 P-dimensional subspace of the relevant e A/2l 2 P-dimensional Hilbert space; (iii) internal dynamics of the horizon is such that an infalling observer finds a smooth horizon with a probability of 1 if a state stays in this subspace. We identify the structure of local operators responsible for describing semi-classical physics in the exterior and interior spacetime regions, and show that this structure avoids the arguments for firewalls-the horizon can keep being smooth throughout the evolution. We discuss the fate of infalling observers under various circumstances, especially when the observers manipulate degrees of freedom before entering the horizon, and we find that an observer can never see a firewall by making a measurement on early Hawking radiation. We also consider the presented framework from the viewpoint of an infalling reference frame, and argue that Minkowski-like vacua are not unique. In particular, the number of true Minkowski vacua is infinite, although the label discriminating these vacua cannot be accessed in usual non-gravitational quantum field theory. An application of the framework to de Sitter horizons is also discussed.

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References (192)

  1. Abrahams, A.M., Rezzolla, L., Rupright, M.E., Anderson, A., Anninos, P., Baumgarte, T.W., Bishop, N.T., Brandt, S.R., Browne, J.C., Camarda, K., Choptuik, M.W., Cook, G.B., Evans, C.R., Finn, L.S., Fox, G., Gómez, R., Haupt, T., Huq, M.F., Kidder, L.E., Klasky, S., Laguna, P., Landry, W., Lehner, L., Lenaghan, J., Marsa, R.L., Massó, J., Matzner, R.A., Mitra, S., Papadopoulos, P., Parashar, M., Saied, F., Saylor, P.E., Scheel, M.A., Seidel, E., Shapiro, S.L., Shoemaker, D.M., Smarr, L.L., Szilágyi, B., Teukolsky, S.A., van Putten, M.H.P.M., Walker, P., Winicour, J., and York Jr, J.W. (The Binary Black Hole Grand Challenge Alliance), "Gravitational wave extraction and outer boundary conditions by perturbative matching", Phys. Rev. Lett., 80, 1812-1815, (1998). For a related online version see: A.M. Abrahams, et al., (September, 1997), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9709082.
  2. Alcubierre, M., Benger, W., Brügmann, B., Lanfermann, G., Nerger, L., Seidel, E., and Takahashi, R., "3D Grazing Collision of Two Black Holes", Phys. Rev. Lett., 87, 271103-1-4, (2001). For a related online version see: M. Alcubierre, et al., (December, 2000), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0012079.
  3. Alcubierre, M., Brügmann, B., Pollney, D., Seidel, E., and Takahashi, R., "Black hole excision for dynamic black holes", Phys. Rev. D, 64, 061501-1-5, (2001). For a related online version see: M. Alcubierre, et al., (April, 2001), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0104020.
  4. Andrade, Z., Beetle, C., Blinov, A., Bromley, B., Burko, L.M., Cranor, M., Owen, R., and Price, R.H., "Periodic standing-wave approximation: Overview and three-dimensional scalar models", Phys. Rev. D, 70, 064001-1-14, (2003).
  5. Anninos, P., Bernstein, D., Brandt, S., Hobill, D., Seidel, E., and Smarr, L.L., "Dynamics of Black Hole Apparent Horizons", Phys. Rev. D, 50, 3801-3819, (1994).
  6. Anninos, P., Camarda, K., Libson, J., Massó, J., Seidel, E., and Suen, W.-M., "Finding apparent horizons in dynamic 3D numerical spacetimes", Phys. Rev. D, 58, 24003-1-12, (1998). For a related online version see: P. Anninos, et al., (September, 1996), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9609059.
  7. Arnowitt, R., Deser, S., and Misner, C.W., "The dynamics of general relativity", in Witten, L., ed., Gravitation: An introduction to current research, 227-265, (Wiley, New York, U.S.A., 1962).
  8. Ashtekar, A., "Black Hole Entropy: Inclusion of Distortion and Angu- lar Momentum", (2003), [Online Presentation]: cited on 22 November 2004, http://www.phys.psu.edu/events/index.html?event id=517.
  9. Ashtekar, A., Personal communication to Corichi, A., Kleihaus, B., and Kunz, J., (2002).
  10. Ashtekar, A., Baez, J., Corichi, A., and Krasnov, K., "Quantum geometry and black hole entropy", Phys. Rev. Lett., 80, 904-907, (1998). For a related online version see: A. Ashtekar, et al., (1997), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9710007.
  11. Ashtekar, A., Baez, J., and Krasnov, K., "Quantum Geometry of Isolated Horizons and Black Hole Entropy", Adv. Theor. Math. Phys., 4, 1-94, (2000). For a related online version see: A. Ashtekar, et al., (2000), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0005126.
  12. Ashtekar, A., Beetle, C., Dreyer, O., Fairhurst, S., Krishnan, B., Lewandowski, J., and Wisniewski, J., "Generic isolated horizons and their applications", Phys. Rev. Lett., 85, 3564-3567, (2000). For a related online version see: A. Ashtekar, et al., (2000), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0006006.
  13. Ashtekar, A., Beetle, C., and Fairhurst, S., "Isolated Horizons: A Generalization of Black Hole Mechanics", Class. Quantum Grav., 16, L1-L7, (1999). For a related online version see: A. Ashtekar, et al., (1998), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9812065.
  14. Ashtekar, A., Beetle, C., and Fairhurst, S., "Mechanics of isolated horizons", Class. Quantum Grav., 17, 253-298, (2000). For a related online version see: A. Ashtekar, et al., (1999), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr- qc/9907068.
  15. Ashtekar, A., Beetle, C., and Lewandowski, J., "Mechanics of rotating isolated horizons", Phys. Rev. D, 64, 044016-1-17, (2001). For a related online version see: A. Ashtekar, et al., (2001), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0103026.
  16. Ashtekar, A., Beetle, C., and Lewandowski, J., "Geometry of generic isolated hori- zons", Class. Quantum Grav., 19, 1195-1225, (2002). For a related online version see: A. Ashtekar, et al., (2001), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0111067.
  17. Ashtekar, A., and Bojowald, M., in preparation.
  18. Ashtekar, A., Bombelli, L., and Reula, O.A., "Covariant phase space of asymptotically flat gravitational fields", in Francaviglia, M., and Holm, D., eds., Mechanics, Analysis and Ge- ometry: 200 Years after Lagrange, 417-450, North-Holland Delta Series, (North Holland, Amsterdam, Netherlands; New York, U.S.A., 1990).
  19. Ashtekar, A., and Corichi, A., "Laws governing isolated horizons: Inclusion of dilaton cou- pling", Class. Quantum Grav., 17, 1317-1332, (2000). For a related online version see: A. Ashtekar, et al., (October, 1999), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9910068.
  20. Ashtekar, A., and Corichi, A., "Non-minimal couplings, quantum geometry and black hole entropy", Class. Quantum Grav., 20, 4473-4484, (2003).
  21. Ashtekar, A., Corichi, A., and Sudarsky, D., "Hairy black holes, horizon mass and solitons", Class. Quantum Grav., 18, 919-940, (2001). For a related online version see: A. Ashtekar, et al., (November, 2000), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0011081.
  22. Ashtekar, A., Corichi, A., and Sudarsky, D., "Non-Minimally Coupled Scalar Fields and Isolated Horizons", Class. Quantum Grav., 20, 3513-3425, (2003).
  23. Ashtekar, A., Dreyer, O., and Wisniewski, J., "Isolated Horizons in 2+1 Gravity", Adv. Theor. Math. Phys., 6, 507-555, (2002). For a related online version see: A. Ashtekar, et al., (June, 2002), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0206024.
  24. Ashtekar, A., Engle, J., Pawlowski, T., and van den Broeck, C., "Multipole moments of isolated horizons", Class. Quantum Grav., 21, 2549-2570, (2004). For a related online version see: A. Ashtekar, et al., (January, 2004), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0401114.
  25. Ashtekar, A., Engle, J., and Van den Broek, C., "Quantum geometry of isolated horizons and black hole entropy: Inclusion of distortion and rotation", (December, 2004), [Online Los Alamos Archive Preprint]: cited on 13 December 2004, http://arXiv.org/abs/gr-qc/0412003.
  26. Ashtekar, A., Fairhurst, S., and Krishnan, B., "Isolated horizons: Hamiltonian evolution and the first law", Phys. Rev. D, 62, 104025-1-29, (2000). For a related online version see: A. Ashtekar, et al., (2000), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0005083.
  27. Ashtekar, A., and Galloway, G., in preparation, (2004).
  28. Ashtekar, A., Hayward, S.A., and Krishnan, B., in preparation.
  29. Ashtekar, A., and Krasnov, K., "Quantum Geometry and Black Holes", in Iyer, B., and Bhawal, B., eds., Black Holes, Gravitational Radiation and the Universe: Essays in Honor of C.V. Vishveshwara, volume 100 of Fundamental Theories of Physics, 149-170, (Kluwer, Dordrecht, Netherlands; Boston, U.S.A., 1999). For a related online version see: A. Ashtekar, et al., (April, 1998), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9804039.
  30. Ashtekar, A., and Krishnan, B., "Dynamical Horizons: Energy, Angular Momentum, Fluxes, and Balance Laws", Phys. Rev. Lett., 89, 261101-1-4, (2002). For a related online version see: A. Ashtekar, et al., (2002), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0207080.
  31. Ashtekar, A., and Krishnan, B., "Dynamical horizons and their properties", Phys. Rev. D, 68, 104030-1-25, (2003). For a related online version see: A. Ashtekar, et al., (2003), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0308033.
  32. Ashtekar, A., and Lewandowski, J., "Background independent quantum gravity: A status report", Class. Quantum Grav., 21, R53-R152, (2004). For a related online version see: A. Ashtekar, et al., (April, 2004), [Online Los Alamos Archive Preprint]: cited on 22 Novem- ber 2004, http://arXiv.org/abs/gr-qc/0404018.
  33. Ashtekar, A., and Streubel, M., "Symplective geometry of radiative fields at null infinity", Proc. R. Soc. London, Ser. A, 376, 585-607, (1981).
  34. Baiotti, L., Hawke, I., Montero, P.J., Löffler, F., Rezzolla, L., Stergioulas, N., Font, J.A., and Seidel, E., "Three-dimensional relativistic simulations of rotating neutron star collapse to a black hole", (March, 2004), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0403029.
  35. Bardeen, J.M., Carter, B., and Hawking, S.W., "The four laws of black hole mechanics", Commun. Math. Phys., 31, 161-170, (1973).
  36. Barreira, M., Carfora, M., and Rovelli, C., "Physics with non-perturbative quantum gravity: Radiation from a quantum black hole", Gen. Relativ. Gravit., 28, 1293-1299, (1996).
  37. Bartnik, R., and Isenberg, J.A., "Summary of spherically symmetric dynamical horizons", Personal communication to A. Ashtekar.
  38. Bartnik, R., and McKinnon, J., "Particlelike solutions of the Einstein-Yang-Mills Equa- tions", Phys. Rev. Lett., 61, 141-144, (1988).
  39. Baumgarte, T.W., "Innermost stable circular orbit of binary black holes", Phys. Rev. D, 62, 024018-1-8, (July, 2000). For a related online version see: T.W. Baumgarte, (April, 2000), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr- qc/0004050.
  40. Beig, R., "The multipole expansion in general relativity", Acta Phys. Austriaca, 53, 249-270, (1981).
  41. Beig, R., and Simon, W., "Proof of a multipole conjecture due to Geroch", Commun. Math. Phys., 78, 1163-1171, (1980).
  42. Beig, R., and Simon, W., "On the multipole expansion of stationary spacetimes", Proc. R. Soc. London, Ser. A, 376, 333-341, (1981).
  43. Beig, R., and Simon, W., "The multipole structure of stationary spacetimes", J. Math. Phys., 24, 1163-1171, (1983).
  44. Bekenstein, J.D., "Black Holes and Entropy", Phys. Rev. D, 7, 2333-2346, (1973).
  45. Bekenstein, J.D., "Generalized second law of thermodynamics in black-hole physics", Phys. Rev. D, 9, 3292-3300, (1974).
  46. Bekenstein, J.D., and Meisels, A., "Einstein A and B coefficients for a black hole", Phys. Rev. D, 15, 2775-2781, (1977).
  47. Ben-Dov, I., "The Penrose inequality and apparent horizons", (August, 2004), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0408066.
  48. Beyer, F., Krishnan, B., and Schnetter, E., in preparation.
  49. Bizoń, P., "Colored Black Holes", Phys. Rev. Lett., 64, 2844-2847, (1990).
  50. Bizoń, P., and Chmaj, T., "Gravitating skyrmions", Phys. Lett. B, 297, 55-62, (1992).
  51. Bizoń, P., and Chmaj, T., "Remark on formation of colored black holes via fine-tuning", Phys. Rev. D, 61, 067501-1-2, (2000). For a related online version see: P. Bizoń, et al., (June, 1999), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr- qc/9906070.
  52. Bizoń, P., and Wald, R.M., "The n=1 colored black hole is unstable", Phys. Lett. B, 267, 173-174, (1991).
  53. Blackburn, J.K., and Detweiler, S., "Close black-hole binary systems", Phys. Rev. D, 46, 2318-2333, (1992).
  54. Bondi, H., van der Burg, M.G.J., and Metzner, A.W.K., "Gravitational waves in general relativity VII: Waves from axi-symmetric isolated systems", Proc. R. Soc. London, Ser. A, 269, 21, (1962).
  55. Booth, I., "Metric-based Hamiltonians, null boundaries, and isolated horizons", Class. Quan- tum Grav., 18, 4239-4264, (2001). For a related online version see: I. Booth, (May, 2001), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr- qc/0105009.
  56. Booth, I., and Fairhurst, S., "The First Law for Slowly Evolving Horizons", Phys. Rev. Lett., 92, 011102-1-4, (2004). For a related online version see: I. Booth, et al., (2003), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0307087.
  57. Bowen, J.M., and York Jr, J.W., "Time-asymmetric initial data for black holes and black-hole collisions", Phys. Rev. D, 21, 2047-2056, (1980).
  58. Brandt, S.R., Correll, R.R., Gómez, R., Huq, M.F., Laguna, P., Lehner, L., Marronetti, P., Matzner, R., Neilsen, D., Pullin, J., Schnetter, E., Shoemaker, D.M., and Winicour, J., "Grazing collision of black holes via the excision of singularities", Phys. Rev. Lett., 85, 5496-5499, (2000). For a related online version see: S.R. Brandt, et al., (September, 2000), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr- qc/0009047.
  59. Bray, H., "Proof of the Riemannian Penrose inequality using the positive mass theorem", J. Differ. Geom., 59, 177, (2001).
  60. Breitenlohner, P., Forgács, P., and Maison, D., "On static spherically symmetric solutions of the Einstein-Yang-Mills equations", Commun. Math. Phys., 163, 141-172, (1994).
  61. Breitenlohner, P., Forgács, P., and Maison, D., "Gravitating monopole solutions II", Nucl. Phys. B, 442, 126-156, (1995).
  62. Bretón, N., "Born-Infeld black hole in the isolated horizon framework", Phys. Rev. D, 67, 124004-1-4, (2003). For a related online version see: N. Bretón, (January, 2003), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/hep- th/0301254.
  63. Brill, D.R., and Lindquist, R.W., "Interaction Energy in Geometrostatics", Phys. Rev., 131, 471-476, (1963).
  64. Brügmann, B., Tichy, W., and Jansen, N., "Numerical Simulation of Orbiting Black Holes", Phys. Rev. Lett., 92, 211101, (2004). For a related online version see: B. Brügmann, et al., (December, 2003), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0312112.
  65. Carter, B., "Black hole equilibrium states", in DeWitt, C., and DeWitt, B.S., eds., Black Holes: Based on lectures given at the 23rd session of the Summer School of Les Houches, 1972, 57-214, (Gordon and Breach, New York, U.S.A., 1973).
  66. Chandrasekhar, S., The Mathematical Theory of Black Holes, volume 69 of The International Series of Monographs on Physics, (Clarendon Press, Oxford, U.K., 1983).
  67. Choptuik, M.W., "Universality and scaling in gravitational collapse of a massless scalar field", Phys. Rev. Lett., 70, 9-12, (1993).
  68. Chruściel, P.T., "On the global structure of Robinson-Trautman space-time", Proc. R. Soc. London, Ser. A, 436, 299-316, (1992).
  69. Chruściel, P.T., "No Hair Theorems Folklore, Conjectures, Results", in Beem, J.K., and Duggal, K.L., eds., Differential Geometry and Mathematical Physics: AMS-CMS Special Session on Geometric Methods in Mathematical Physics, August 15-19, 1993, Vancouver, British Columbia, Canada, volume 170 of Contemporary Mathematics, 23-49, (American Mathematical Society, Providence, U.S.A., 1994).
  70. Cook, G.B., "Initial Data for Numerical Relativity", Living Rev. Relativity, 2, (2000), [Online Journal Article]: cited on 22 November 2004, http://www.livingreviews.org/lrr-2000-5.
  71. Cook, G.B., "Three-dimensional initial data for the collision of two black holes II: Quasicir- cular orbits for equal mass black holes", Phys. Rev. D, 50, 5025-5032, (October, 1994). For a related online version see: G.B. Cook, (April, 1994), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9404043.
  72. Cook, G.B., "Corotating and irrotational binary black holes in quasicircular orbits", Phys. Rev. D, 65, 084003-1-13, (2002). For a related online version see: G.B. Cook, (August, 2001), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr- qc/0108076.
  73. Cook, G.B., Huq, M.F., Klasky, S.A., Scheel, M.A., Abrahams, A.M., Anderson, A., Anninos, P., Baumgarte, T.W., Bishop, N.T., Brandt, S.R., Browne, J.C., Camarda, K., Choptuik, M.W., Evans, C.R., Finn, L.F., Fox, G.C., Gómez, R., Haupt, T., Kidder, L.E., Laguna, P., Landry, W., Lehner, L., Lenaghan, J., Marsa, R.L., Massó, J., Matzner, R.A., Mitra, S., Papadopoulos, P., Parashar, M., Rezzolla, L., Rupright, M.E., Saied, F., Saylor, P.E., Seidel, E., Shapiro, S.L., Shoemaker, D.M., Smarr, L.L., Suen, W.-M., Szilágyi, B., Teukolsky, S.A., van Putten, M.H.P.M., Walker, P., Winicour, J., and York Jr, J.W. (Binary Black Hole Grand Challenge Alliance), "Boosted Three-Dimensional Black-Hole Evolutions with Singularity Excision", Phys. Rev. Lett., 80, 2512-2516, (1998). For a related online version see: G.B. Cook, et al., (November, 1997), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9711078\. Binary Black Hole Grand Challenge Alliance.
  74. Cook, G.B., and Pfeiffer, H.P., "Excision boundary conditions for black-hole initial data", Phys. Rev. D, 70, 104016-1-24, (2004).
  75. Corichi, A., Nucamendi, U., and Sudarsky, D., "Einstein-Yang-Mills isolated horizons: Phase space, mechanics, hair, and conjectures", Phys. Rev. D, 62, 044046-1-19, (2000). For a related online version see: A. Corichi, et al., (February, 2000), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0002078.
  76. Corichi, A., Nucamendi, U., and Sudarsky, D., "Mass formula for Einstein-Yang-Mills soli- tons", Phys. Rev. D, 64, 107501-1-4, (2001). For a related online version see: A. Corichi, et al., (June, 2001), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0106084.
  77. Corichi, A., and Sudarsky, D., "Mass of colored black holes", Phys. Rev. D, 61, 101501-1-4, (2000). For a related online version see: A. Corichi, et al., (December, 1999), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9912032.
  78. Cutler, C., and Thorne, K.S., "An Overview of Gravitational-Wave Sources", in Bishop, N.T., and Maharaj, S.D., eds., General Relativity and Gravitation: Proceedings of the 16th International Conference on General Relativity and Gravitation, Durban, South Africa, 15- 21 July 2001, 72-111, (World Scientific, Singapore; River Edge, U.S.A., 2002). For a related online version see: C. Cutler, et al., (April, 2002), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0204090.
  79. Dain, S., "Black hole interaction energy", Phys. Rev. D, 66, 084019-1-8, (2002). For a related online version see: S. Dain, (July, 2002), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0207090.
  80. Dain, S., "Trapped surfaces as boundaries for the constraint equations", Class. Quantum Grav., 21, 555-574, (2004). For a related online version see: S. Dain, (August, 2003), [On- line Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr- qc/0308009.
  81. Dain, S., Jaramillo, J.L., and Krishnan, B.
  82. Diener, P., personal communication to B. Krishnan.
  83. Diener, P., "A new general purpose event horizon finder for 3D numerical spacetimes", Class. Quantum Grav., 20, 4901-4918, (2003). For a related online version see: P. Diener, (2003), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr- qc/0305039.
  84. Domagala, M., and Lewandowski, J., "Black-hole entropy from quantum geometry", Class. Quantum Grav., 21, 5233-5243, (2004). For a related online version see: M. Doma- gala, et al., (2004), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0407051.
  85. Dreyer, O., Krishnan, B., Schnetter, E., and Shoemaker, D.M., "Introduction to isolated horizons in numerical relativity", Phys. Rev. D, 67, 024018-1-14, (2003). For a related online version see: O. Dreyer, et al., (June, 2002), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0206008.
  86. Eardley, D.M., "Black Hole Boundary Conditions and Coordinate Conditions", Phys. Rev. D, 57, 2299-2304, (1998). For a related online version see: D.M. Eardley, (1997), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9703027.
  87. Ernst, F.J., "Black holes in a magnetic universe", J. Math. Phys., 17, 54-56, (1976).
  88. Fairhurst, S., and Krishnan, B., "Distorted black holes with charge", Int. J. Mod. Phys. D, 10, 691-710, (2001). For a related online version see: S. Fairhurst, et al., (October, 2000), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr- qc/0010088.
  89. Finn, L.S., Personal communication to A. Ashtekar.
  90. Friedman, J.L., Schleich, K., and Witt, D.M., "Topological censorship", Phys. Rev. Lett., 71, 1486-1489, (1993). For a related online version see: J.L. Friedman, et al., (May, 1993), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr- qc/9305017. Erratum: Phys. Rev. Lett. 75 (1995) 1872.
  91. Friedman, J.L., Uryū, K., and Shibata, M., "Thermodynamics of binary black holes and neutron stars", Phys. Rev. D, 65, 064035-1-20, (2002). For a related online version see: J.L. Friedman, et al., (June, 2001), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0108070.
  92. Friedrich, H., "On the regular and asymptotic characteristic initial value problem for Ein- stein's field equations", Proc. R. Soc. London, Ser. A, 375, 169-184, (1981).
  93. Galloway, G.J., personal communication to A. Ashtekar, (2004).
  94. Gambini, R., Obregón, O., and Pullin, J., "Yang-Mills analogs of the Immirzi ambigu- ity", Phys. Rev. D, 59, 047505-1-4, (1999). For a related online version see: R. Gam- bini, et al., (2001), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9801055.
  95. Garfinkle, D., Horowitz, G.T., and Strominger, A., "Charged black holes in string theory", Phys. Rev. D, 43, 3140-3143, (1991).
  96. Garfinkle, D., Horowitz, G.T., and Strominger, A., "Erratum: Charged black holes in string theory", Phys. Rev. D, 45, 3888, (1992).
  97. Geroch, R., "Multipole moments II. Curved space", J. Math. Phys., 11, 2580-2588, (1970).
  98. Geroch, R., and Hartle, J.B., "Distorted Black Holes", J. Math. Phys., 23, 680, (1982).
  99. Gibbons, G.W., and Hawking, S.W., "Cosmological event horizons, thermodynamics, and particle creation", Phys. Rev. D, 15, 2738-2751, (1977).
  100. Gibbons, G.W., Kallosh, R.E., and Kol, B., "Moduli, Scalar Charges, and the First Law of Black Hole Thermodynamics", Phys. Rev. Lett., 77, 4992-4995, (1996).
  101. Gibbons, G.W., and Maeda, K., "Black holes and membranes in higher-dimensional theories with dilaton fields", Nucl. Phys. B, 298, 741-775, (1998).
  102. Gonzalez, J., and van den Broeck, C., in preparation.
  103. Gourgoulhon, E., Grandclément, P., and Bonazzola, S., "Binary black holes in circular orbits. I. A global spacetime approach", Phys. Rev. D, 65, 044020-1-19, (2002). For a related online version see: E. Gourgoulhon, et al., (June, 2001), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0106015.
  104. Grandclément, P., Gourgoulhon, E., and Bonazzola, S., "Binary black holes in circular orbits. II. Numerical methods and first results", Phys. Rev. D, 65, 044021-1-18, (2002). For a related online version see: P. Grandclément, et al., (June, 2001), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0106016.
  105. Gundlach, C., "Critical phenomena in gravitational collapse", Adv. Theor. Math. Phys., 2, 1-49, (1998). For a related online version see: C. Gundlach, (December, 1997), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9712084.
  106. Háj íček, P., "Stationary electrovacuum spacetimes with bifurcate horizons", J. Math. Phys., 16, 518-522, (1975).
  107. Hansen, R., "Multipole moments in stationary space-times", J. Math. Phys., 15, 46-52, (1974).
  108. Hartle, J.B., and Hawking, S.W., "Energy and Angular Momentum Flow in to a Black Hole", Commun. Math. Phys., 27, 283-290, (1972).
  109. Hartmann, B., Kleihaus, B., and Kunz, J., "Axially symmetric monopoles and black holes in Einstein-Yang-Mills-Higgs theory", Phys. Rev. D, 65, 024027-1-22, (2002). For a related online version see: B. Hartmann, et al., (2001), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/hep-th/0108129.
  110. Hawking, S.W., "Black Holes in General Relativity", Commun. Math. Phys., 25, 152, (1972).
  111. Hawking, S.W., "The event horizon", in DeWitt, C., and DeWitt, B.S., eds., Black Holes: Based on lectures given at the 23rd session of the Summer School of Les Houches, 1972, 1-56, (Gordon and Breach, New York, U.S.A., 1973).
  112. Hawking, S.W., "Particle Creation by Black Holes", Commun. Math. Phys., 43, 199, (1975).
  113. Hawking, S.W., and Ellis, G.F.R., The Large Scale Structure of Space-Time, Cambridge Monographs on Mathematical Physics, (Cambridge University Press, Cambridge, U.K., 1973).
  114. Hawking, S.W., and Hunter, C.J., "Gravitational entropy and global structure", Phys. Rev. D, 59, 044025-1-10, (1999). For a related online version see: S.W. Hawking, et al., (1998), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/hep-th/9808085.
  115. Hayward, S., "Energy and entropy conservation for dynamical black holes", Phys. Rev. D, 70, 104027-1-13, (2004). For a related online version see: S. Hayward, (August, 2004), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr- qc/0408008.
  116. Hayward, S.A., "Energy conservation for dynamical black holes", (April, 2004), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0404077.
  117. Hayward, S.A., "General laws of black-hole dynamics", Phys. Rev. D, 49, 6467-6474, (1994). For a related online version see: S.A. Hayward, (1993), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9303006.
  118. Hayward, S.A., "Spin-Coefficient Form of the New Laws of Black-Hole Dynamics", Class. Quantum Grav., 11, 3025-3036, (1994). For a related online version see: S.A. Hayward, (1994), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9406033.
  119. Heusler, M., Black Hole Uniqueness Theorems, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1996).
  120. Horowitz, G.T., "Quantum States of Black Holes", in Wald, R.M., ed., Black Holes and Relativistic Stars, 241-266, (University of Chicago Press, Chicago, U.S.A., 1998).
  121. Hughes, S.A., Keeton II, C.R., Walker, P., Walsh, K.T., Shapiro, S.L., and Teukolsky, S.A., "Finding black holes in numerical spacetimes", Phys. Rev. D, 49, 4004-4015, (1994).
  122. Huisken, G., and Ilmanen, T., "The inverse mean curvature flow and the Riemannian Penrose inequality", J. Differ. Geom., 59, 353, (2001).
  123. Jacobson, T., Kang, G., and Myers, R.C., "On black hole entropy", Phys. Rev. D, 49, 6587-6598, (1994).
  124. Jaramillo, J.L., Gourgoulhon, E., and Mena Marugán, G.A., "Inner boundary conditions for black hole Initial Data derived from Isolated Horizons", (2004), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0407063.
  125. Kastor, D., and Traschen, J., "Cosmological multi-black-hole solutions", Phys. Rev. D, 47, 5370-5375, (1993).
  126. Khanna, G., Baker, J., Gleiser, R.J., Laguna, P., Nicasio, C.O., Nollert, H.-P., Price, R.H., and Pullin, J., "Inspiraling Black Holes: The Close Limit", Phys. Rev. Lett., 83, 3581-3584, (1999). For a related online version see: G. Khanna, et al., (May, 1999), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9905081.
  127. Kleihaus, B., and Kunz, J., "Static Black-Hole Solutions with Axial Symmetry", Phys. Rev. Lett., 79, 1595-1598, (1997).
  128. Kleihaus, B., and Kunz, J., "Static axially symmetric Einstein-Yang-Mills-Dilaton solutions: 1. Regular solutions", Phys. Rev. D, 57, 843-856, (1998).
  129. Kleihaus, B., and Kunz, J., "Static axially symmetric Einstein-Yang-Mills-Dilaton solutions: 2. Black hole solutions", Phys. Rev. D, 57, 6138-6157, (1998).
  130. Kleihaus, B., and Kunz, J., "Non-Abelian black holes with magnetic dipole hair", Phys. Lett. B, 494, 130-134, (2000). For a related online version see: B. Kleihaus, et al., (2000), [On- line Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/hep- th/0008034.
  131. Kleihaus, B., Kunz, J., and Navarro-Lérida, F., "Rotating dilaton black holes with hair", Phys. Rev. D, 69, 064028-1-30, (2004). For a related online version see: B. Kleihaus, et al., (June, 2003), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0306058.
  132. Kleihaus, B., Kunz, J., Sood, A., and Wirschins, M., "Horizon properties of Einstein-Yang- Mills black hole", Phys. Rev. D, 65, 061502-1-4, (2002).
  133. Korzynski, N., Lewandowski, J., and Pawlowski, T., "Mechanics of isolated horizons in higher dimensions", in preparation.
  134. Krasnov, K., "Geometrical entropy from loop quantum gravity", Phys. Rev. D, 55, 3505- 3513, (1997).
  135. Krasnov, K., "On statistical mechanics of Schwarzschild black holes", Gen. Relativ. Gravit., 30, 53-68, (1998).
  136. Krishnan, B., Isolated Horizons in Numerical Relativity, PhD Thesis, (The Penn- sylvania State University, University Park, U.S.A., 2002). For a related online ver- sion see: B. Krishnan, (2002), [Online Thesis]: cited on 22 November 2004, http://etda.libraries.psu.edu/theses/approved/WorldWideIndex/ETD-177/.
  137. Kuroda, Y., "Naked Singularities in the Vaidya Spacetimee", Prog. Theor. Phys., 72, 63-72, (1984).
  138. Lehner, L., "Numerical Relativity: A review", Class. Quantum Grav., 18, R25-R86, (2001). For a related online version see: L. Lehner, (June, 2001), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0106072.
  139. Lehner, L., Bishop, N.T., Gómez, R., Szilágyi, B., and Winicour, J., "Exact solutions for the intrinsic geometry of black hole coalescence", Phys. Rev. D, 60, 044005-1-10, (1999). For a related online version see: L. Lehner, et al., (September, 1998), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9809034.
  140. Lewandowski, J., "Spacetimes admitting isolated horizons", Class. Quantum Grav., 17, L53- L59, (2000). For a related online version see: J. Lewandowski, (July, 1999), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9907058.
  141. Lewandowski, J., and Pawlowski, T., "Quasi-local rotating black holes in higher dimension: geometry", (October, 2004), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0410146.
  142. Lewandowski, J., and Pawlowski, T., "Geometric characterizations of the Kerr isolated horizon", Int. J. Mod. Phys. D, 11, 739-746, (2001). For a related online version see: J. Lewandowski, et al., (December, 2001), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0101008.
  143. Lewandowski, J., and Pawlowski, T., "Extremal isolated horizons: a local uniqueness theorem", Class. Quantum Grav., 20, 587-606, (2003). For a related online version see: J. Lewandowski, et al., (August, 2002), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0208032.
  144. Lichnerowicz, A., "L'integration des équations de la gravitation relativiste et le probléme des n corps", J. Math. Pures Appl., 23, 37-63, (1944).
  145. Maldacena, J., and Strominger, A., "Statistical entropy of four-dimensional extremal black holes", Phys. Rev. Lett., 77, 428-429, (1996). For a related online version see: J. Maldacena, et al., (March, 1996), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/hep-th/9603060.
  146. Mann, R.B., "Misner string entropy", Phys. Rev. D, 60, 104047-1-5, (1999). For a related online version see: R.B. Mann, (March, 1999), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/hep-th/9903229.
  147. Mann, R.B., and Garfinkle, D., "Generalized entropy and Noether charge", Class. Quantum Grav., 17, 3317-3324, (2000). For a related online version see: R.B. Mann, et al., (2000), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr- qc/0004056.
  148. Masood-ul Alam, A.K.M., "Uniqueness of a static charged dilaton black hole", Class. Quan- tum Grav., 10, 2649-2656, (1993).
  149. Meissner, K.A., "Black-hole entropy in loop quantum gravity", Class. Quantum Grav., 21, 5245-5252, (2004). For a related online version see: K.A. Meissner, (July, 2004), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0407052.
  150. Misner, C.W., "Wormhole Initial Conditions", Phys. Rev., 118, 1110-1111, (1959).
  151. Misner, C.W., "The method of images in geometrostatics", Ann. Phys. (N.Y.), 24, 102-117, (1963).
  152. Nakao, K., Shiromizu, T., and Hayward, S.A., "Horizons of the Kastor-Traschen multi-black- hole cosmos", Phys. Rev. D, 52, 796-808, (1995).
  153. New, K.C.B., "Gravitational Waves from Gravitational Collapse", Living Rev. Relativity, 6, (2003), [Online Journal Article]: cited on 22 November 2004, http://www.livingreviews.org/lrr-2003-2.
  154. Núñez, D., Quevedo, H., and Sudarsky, D., "Black Holes have no Short Hair", Phys. Rev. Lett., 76, 571-574, (1996). For a related online version see: D. Núñez, et al., (January, 1996), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr- qc/9601020.
  155. Pawlowski, T., Lewandowski, J., and Jezierski, J., "Spacetimes foliated by Killing horizons", Class. Quantum Grav., 21, 1237-1252, (2004). For a related online version see: T. Pawlowski, et al., (June, 2003), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0306107.
  156. Pejerski, D.W., and Newman, E.T., "Trapped surface and the development of singularities", J. Math. Phys., 9, 1929-1937, (1971).
  157. Penrose, R., "Naked singularities", Ann. N.Y. Acad. Sci., 224, 125-134, (1973).
  158. Pfeiffer, H.P., Cook, G.B., and Teukolsky, S.A., "Comparing initial-data sets for binary black holes", Phys. Rev. D, 66, 024047-1-17, (2002). For a related online version see: H.P. Pfeiffer, et al., (June, 2002), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0203085.
  159. Pfeiffer, H.P., Teukolsky, S.A., and Cook, G.B., "Quasicircular orbits for spinning binary black holes", Phys. Rev. D, 62, 104018-1-11, (2000). For a related online version see: H.P. Pfeiffer, et al., (June, 2000), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0006084.
  160. Pullin, J., "The close limit of colliding black holes: An update", Prog. Theor. Phys. Suppl., 136, 107-120, (1999). For a related online version see: J. Pullin, (September, 1999), [On- line Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr- qc/9909021.
  161. Rendall, A.D., "Reduction of the characteristic initial value problem to the Cauchy problem and its applications to the Einstein equations", Proc. R. Soc. London, Ser. A, 427, 221-239, (1990).
  162. Rovelli, C., "Loop Quantum Gravity", Living Rev. Relativity, 1, (1998), [Online Journal Article]: cited on 22 November 2004, http://www.livingreviews.org/lrr-1998-1.
  163. Rovelli, C., "Black hole entropy from loop quantum gravity", Phys. Rev. Lett., 14, 3288- 3291, (1996).
  164. Rovelli, C., "Loop quantum gravity and black hole physics", Helv. Phys. Acta, 69, 582-611, (1996).
  165. Sachs, R.K., and Bergmann, P.G., "Structure of particles in linearized gravitational theory", Phys. Rev., 112, 674-680, (1958).
  166. Senovilla, J.M.M., "On the existence of horizons in spacetimes with vanishing curvature invariants", J. High Energy Phys., 11, 046, (2003). For a related online version see: J.M.M. Senovilla, (November, 2003), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/hep-th/0311172.
  167. Shapiro, S.L., and Teukolsky, S.A., "Collisions of relativistic clusters and the formation of black holes", Phys. Rev. D, 45, 2739-2750, (1992).
  168. Shoemaker, D.M., Huq, M.F., and Matzner, R.A., "Generic tracking of multiple apparent horizons with level flow", Phys. Rev. D, 62, 124005-1-12, (2000). For a related online version see: D.M. Shoemaker, et al., (April, 2000), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0004062.
  169. Smarr, L.L., "Surface Geometry of Charged Rotating Black Holes", Phys. Rev. D, 7, 289-295, (1973).
  170. Smolin, L., "Linking topological quantum field theory and nonperturbative quantum grav- ity", J. Math. Phys., 36, 6417-6455, (1995).
  171. Smoller, J.A., Wasserman, A.G., and Yau, S.T., "Existence of black hole solutions for the Einstein / Yang-Mills equations", Commun. Math. Phys., 154, 377, (1993).
  172. Straumann, N., and Zhou, Z.H., "Instability of a colored black hole solution", Phys. Lett. B, 243, 33, (1990).
  173. Straumann, N., and Zhou, Z.H., "Instability of the Bartnik-McKinnon solution to the Einstein-Yang-Mills equations", Phys. Lett. B, 237, 353, (1990).
  174. Strominger, A., and Vafa, C., "Microscopic origin of the Bekenstein-Hawking entropy", Phys. Lett. B, 379, 99-104, (1996). For a related online version see: A. Strominger, et al., (January, 1996), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/hep-th/9601029.
  175. Sudarsky, D., and Wald, R.M., "Extrema of mass, stationarity and staticity, and solutions to the Einstein-Yang-Mills equations", Phys. Rev. D, 46, 1453-1474, (1992).
  176. Thiemann, T., "Introduction to modern canonical quantum general relativity", (Oc- tober, 2001), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0110034.
  177. Thornburg, J., "A fast apparent horizon finder for 3-dimensional Cartesian grids in numerical relativity", Class. Quantum Grav., 21, 743-766, (2004). For a related online version see: J. Thornburg, (June, 2003), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/0306056.
  178. Torii, T., and Maeda, K., "Black holes with non-Abelian hair and their thermodynamical properties", Phys. Rev. D, 48, 1643-1651, (1993).
  179. Vaidya, P.C., "The gravitational field of a radiating star", Proc. Indian Acad. Sci., Sect. A, 33, 264, (1951).
  180. van den Broeck, C., personal communication to A. Ashtekar.
  181. Volkov, M.S., and Gal'tsov, D.V., "Gravitating non-Abelian solitons and black holes with Yang-Mills fields", Phys. Rep., 319, 1, (1999).
  182. Wald, R.M., "The Thermodynamics of Black Holes", Living Rev. Relativity, 4, (July, 2001), [Online Journal Article]: cited on 22 November 2004, http://www.livingreviews.org/lrr-2001- 6.
  183. Wald, R.M., "Black hole entropy is the Noether charge", Phys. Rev. D, 48, R3427-R3431, (1993).
  184. Wald, R.M., and Iyer, V., "Some properties of the Noether charge and a proposal for dy- namical black hole entropy", Phys. Rev. D, 50, 846-864, (1994).
  185. Wald, R.M., and Zoupas, A., "General definition of "conserved quantities" in general relativ- ity and other theories of gravity", Phys. Rev. D, 61, 084027-1-16, (2000). For a related on- line version see: R.M. Wald, et al., (November, 1999), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9911095.
  186. Waugh, B., and Lake, K., "Double-null coordibates for the Vaidya spacetime", Phys. Rev. D, 34, 2978-2984, (1986).
  187. Wheeler, J.A., "It from Bit", in Keldysh, L.V., and Feinberg, V.Y., eds., Sakharov Memorial Lectures on Physics: Proceedings of the First International Sakharov Conferenference on Physics, Volume 2, (Nova Science, New York, U.S.A., 1992).
  188. Witten, E., "A new proof of the positive energy theorem", Commun. Math. Phys., 80, 381- 402, (1981).
  189. Wolfram Research, Inc., "Mathematica: The Way the World Calcu- lates", (2004), [Online HTML document]: cited on 22 November 2004, http://www.wolfram.com/products/mathematica/index.html.
  190. Yo, H.-J., Cook, J.N., Shapiro, S.L., and Baumgarte, T.W., "Quasi-equilibrium binary black hole initial data for dynamical evolutions", Phys. Rev. D, 70, 084033-1-14, (2004).
  191. York Jr, J.W., "Kinematics and Dynamics of General Relativity", in Small, L.L., ed., Sources of Gravitational Radiation: Proceedings of the Battelle Seattle Workshop, July 24 -August 4, 1978, 83-126, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1979).
  192. York Jr, J.W., "Conformal 'thin-sandwich' data for the initial-value problem of general rel- ativity", Phys. Rev. Lett., 82, 1350-1353, (1999). For a related online version see: J.W. York Jr, (October, 1998), [Online Los Alamos Archive Preprint]: cited on 22 November 2004, http://arXiv.org/abs/gr-qc/9810051.

0 40 70 42 v 1 1 3 Ju l 2 00 4 Isolated and Dynamical Horizons and Their Applications

2004

Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five years a new, quasi-local framework was introduced to analyze diverse facets of black holes in an unified manner. In this framework, evolving black holes are modeled by dynamical horizons and black holes in equilibrium by isolated horizons. We review basic properties of these horizons and summarize applications to mathematical physics, numerical relativity and quantum gravity. This paradigm has led to significant generalizations of several results in black hole physics. Specifically, it has introduced a more physical setting for black hole thermodynamics and for black hole entropy calculations in quantum gravity; suggested a phenomenological model for hairy black holes; pro...

An Introduction to Local Black Hole Horizons in the 3+1 Approach to General Relativity

International Journal of Modern Physics: Conference Series, 2012

We present an introduction to dynamical trapping horizons as quasi-local models for black hole horizons, from the perspective of an Initial Value Problem approach to the construction of generic black hole spacetimes. We focus on the geometric and structural properties of these horizons aiming, as a main application, at the numerical evolution and analysis of black hole spacetimes in astrophysical scenarios. In this setting, we discuss their dual role as an a priori ingredient in certain formulations of Einstein equations and as an a posteriori tool for the diagnosis of dynamical black hole spacetimes. Complementary to the first-principles discussion of quasi-local horizon physics, we place an emphasis on the rigidity properties of these hypersurfaces and their role as privileged geometric probes into near-horizon strong-field spacetime dynamics.

Einstein-Yang-Mills isolated horizons: Phase space, mechanics, hair, and conjectures

Physical Review D, 2000

The concept of "Isolated Horizon" has been recently used to provide a full Hamiltonian treatment of black holes. It has been applied successfully to the cases of {\it non-rotating}, {\it non-distorted} black holes in Einstein Vacuum, Einstein-Maxwell and Einstein-Maxwell-Dilaton Theories. In this note, it is investigated the extent to which the framework can be generalized to the case of non-Abelian gauge theories where `hairy black holes' are known to exist. It is found that this extension is indeed possible, despite the fact that in general, there is no `canonical normalization' yielding a preferred Horizon Mass. In particular the zeroth and first laws are established for all normalizations. Colored static spherically symmetric black hole solutions to the Einstein-Yang-Mills equations are considered from this perspective. A canonical formula for the Horizon Mass of such black holes is found. This analysis is used to obtain nontrivial relations between the masses of the colored black holes and the regular solitonic solutions in Einstein-Yang-Mills theory. A general testing bed for the instability of hairy black holes in general non-linear theories is suggested. As an example, the embedded Abelian magnetic solutions are considered. It is shown that, within this framework, the total energy is also positive and thus, the solutions are potentially unstable. Finally, it is discussed which elements would be needed to place the Isolated Horizons framework for Einstein-Yang-Mills theory in the same footing as the previously analyzed cases. Motivated by these considerations and using the fact that the Isolated Horizons framework seems to be the appropriate language to state uniqueness and completeness conjectures for the EYM equations --in terms of the horizon charges--, two such conjectures are put forward.

Singularity-Free Gravitational Collapse: From Regular Black Holes to Horizonless Objects

2023

Penrose's singularity theorem implies that if a trapped region forms in a gravitational collapse, then a singularity must form as well within such region. However, it is widely expected that singularities should be generically avoided by quantum gravitational effects. Here we shall explore both the minimum requirements to avoid singularities in a gravitational collapse as well as discuss, without relying on a specific quantum gravity model, the possible regular spacetimes associated to such regularization of the spacetime fabric. In particular, we shall expose the intimate and quite subtle relationship between regular black holes, black bounces and their corresponding horizonless object limits. In doing so, we shall devote specific attention to those critical (extremal) black hole configurations lying at the boundary between horizonful and horizonless geometries. While these studies are carried out in stationary configurations, the presence of generic instabilities strongly suggest the need for considering more realistic time-dependent dynamical spacetimes. Missing specific dynamical models, much less rigorous statements can be made for evolving geometries. We shall nonetheless summarize here their present understanding and discuss their implications for future phenomenological studies.

black holes: Universal versus Killing horizons

2014

Black Holes in Lorentz violating theories A. Einstein-AEther theory B. Hořava-Lifshitz gravity C. Einstein-AEther black holes D. A digression on acoustic gravity and Universal horizons III. Physical trajectories in an Einstein-AEther black hole A. Ray tracing and peeling in purely metric black holes B. Rays of constant aether time C. Modified dispersion relations D. A notion of conserved energy E. Physical ray trajectories IV. Near-horizon physics A. Near the Universal horizon B. Near the Killing horizon C. Lingering near the Killing horizon V. Hawking Radiation? VI. Discussion

Farewell to black hole horizons and singularities?

2011

We consider the fundamental issues which dominate the question about the existence or non-existence of black hole horizons and singularities from both of the theoretical and observational points of view, and discuss some of the ways that black hole singularities can be prevented from forming at a classical level, i.e. without arguments of quantum gravity. In this way, we argue that black holes could have a different nature with respect