A toroidal proposal for the Rotating Black Hole model (original) (raw)

Rotating Black Holes, Complex Geometry, and Thermodynamics, b

Annals of The New York Academy of Sciences, 1991

In recent years the proposal' to relate the Euclidean action of black holes to approximations of certain functional integrals that can be interpreted as thermodynamic partition functions has been developed extensively. In this paper we outline briefly the key points of these developments and extend them to the treatment of stationary geometries, in particular the geometries of rotating black holes. Stationary holes are ostensibly more difficult to handle than static ones, primarily because neither the extrinsic curvature of the stationary constant-time slices nor the corresponding shift vector vanishes, while both do vanish in the case of static geometries. Consequently, as we shall see, there is no real Euclidean metric that represents a rotating black hole. Nevertheless, the hole can be described by a complex geometry that is an extremum of an appropriate real action-we shall call it the thermodynamical action.

Rotating black holes, global symmetry and first order formalism

Journal of High Energy Physics, 2012

In this paper we consider axisymmetric black holes in supergravity and address the general issue of defining a first order description for them. The natural setting where to formulate the problem is the De Donder-Weyl-Hamilton-Jacobi theory associated with the effective two-dimensional sigma-model action describing the axisymmetric solutions. We write the general form of the two functions S m defining the first-order equations for the fields. It is invariant under the global symmetry group G (3) of the sigma-model. We also discuss the general properties of the solutions with respect to these global symmetries, showing that they can be encoded in two constant matrices belonging to the Lie algebra of G (3) , one being the Nöther matrix of the sigma model, while the other is non-zero only for rotating solutions. These two matrices allow a G (3)-invariant characterization of the rotational properties of the solution and of the extremality condition. We also comment on extremal, under-rotating solutions from this point of view.

Rotating Black Holes in Unified Theories

Progress of Theoretical Physics Supplement, 1999

Some remarkable properties of the supersymmetric five-dimensional rotating solutions of Beckenridge, Myers, Peet and Vafa are described. The solutions may be under-rotating, in which case they are extreme black holes or over-rotating, in which case they are naked time machines. The geodesics and global structure of the spacetime are analysed, including the possibility of time travel by freely falling observers. I argue, following recent work with C. Herdeiro, that the over-rotating solutions cannot be reached from the under-rotating black hole solutions by a physical process using a finite amount of energy. This would fit in with the Chronology Protection conjecture.

2 The interior structure of rotating black holes 1. Concise derivation

2012

This paper presents a concise derivation of a new set of solutions for the interior structure of accreting, rotating black holes. The solutions are conformally stationary, axisymmetric, and conformally separable. Hyper-relativistic counter-streaming between freely-falling collisionless ingoing and outgoing streams leads to mass inflation at the inner horizon, followed by collapse. The solutions fail at an exponentially tiny radius, where the rotational motion of the streams becomes comparable to their radial motion. The papers provide a fully nonlinear, dynamical solution for the interior structure of a rotating black hole from just above the inner horizon inward, down to a tiny scale.

Rotating Black Holes in Higher Dimensions

AIP Conference Proceedings, 2008

The properties of higher-dimensional black holes can differ significantly from those of black holes in four dimensions, since neither the uniqueness theorem, nor the staticity theorem or the topological censorship theorem generalize to higher dimensions. We first discuss black holes of Einstein-Maxwell theory and Einstein-Maxwell-Chern-Simons theory with spherical horizon topology. Here new types of stationary black holes are encountered. We then discuss nonuniform black strings and present evidence for a horizon topology changing transition.

On the possible spacetime structures of rotating loop quantum black holes

International Journal of Geometric Methods in Modern Physics

To date, a mathematically consistent construction of effective rotating black hole models in the context of Loop Quantum Gravity (LQG) is still lacking. In this work, we start with the assumption that rotating LQG black hole metrics can be effectively obtained using Newman–Janis Algorithm. Then, based on a few extra fair assumptions on the seed metric functions, we make a conjecture on what a rotating LQG black hole would generically look like. Our general arguments and conclusions can be supported by some known specific examples in the literature.

Towards a general description of the interior structure of rotating black holes

Eprint Arxiv 1108 3512, 2011

The purpose of this paper is to present a number of proposals about the interior structure of a rotating black hole that is accreting slowly, but in an arbitrary time-and space-dependent fashion. The proposals could potentially be tested with numerical simulations. Outgoing and ingoing particles free-falling in the parent Kerr geometry become highly focused along the principal outgoing and ingoing null directions as they approach the inner horizon, triggering the mass inflation instability. The original arguments of Barrabés, Israel & Poisson (1990) regarding inflation in rotating black holes are reviewed, and shown to be based on Raychauduri's equation applied along the outgoing and ingoing null directions. It is argued that gravitational waves should behave in the geometric optics limit, and consequently that the spacetime should be almost shear-free. A full set of shear-free equations is derived. A specific line-element is proposed, which is argued should provide a satisfactory approximation during early inflation. Finally, it is argued that super-Planckian collisions between outgoing and ingoing particles will lead to entropy production, bringing inflation to an end, and precipitating collapse.

Rotating black hole, twistor-string and spinning particle

Czechoslovak Journal of Physics, 2005

We discuss basic features of the model of spinning particle based on the Kerr solution. It contains a very nontrivial real stringy structure consisting of the Kerr circular string and an axial stringy system.

Five-dimensional rotating black hole in a uniform magnetic field: The gyromagnetic ratio

Physical Review D, 2004

In four dimensional general relativity, the fact that a Killing vector in a vacuum spacetime serves as a vector potential for a test Maxwell field provides one with an elegant way of describing the behaviour of electromagnetic fields near a rotating Kerr black hole immersed in a uniform magnetic field. We use a similar approach to examine the case of a five dimensional rotating black hole placed in a uniform magnetic field of configuration with bi-azimuthal symmetry, that is aligned with the angular momenta of the Myers-Perry spacetime. Assuming that the black hole may also possess a small electric charge we construct the 5-vector potential of the electromagnetic field in the Myers-Perry metric using its three commuting Killing vector fields. We show that, like its four dimensional counterparts, the five dimensional Myers-Perry black hole rotating in a uniform magnetic field produces an inductive potential difference between the event horizon and an infinitely distant surface. This potential difference is determined by a superposition of two independent Coulomb fields consistent with the two angular momenta of the black hole and two nonvanishing components of the magnetic field. We also show that a weakly charged rotating black hole in five dimensions possesses two independent magnetic dipole moments specified in terms of its electric charge, mass, and angular momentum parameters. We prove that a five dimensional weakly charged Myers-Perry black hole must have the value of the gyromagnetic ratio g = 3.