Abhay Ashtekar | Pennsylvania State University (original) (raw)
Papers by Abhay Ashtekar
Physical Review Letters, 2012
Since the standard inflationary paradigm is based on quantum field theory on classical space-time... more Since the standard inflationary paradigm is based on quantum field theory on classical space-times, it excludes the Planck era. Using techniques from loop quantum gravity, the paradigm is extended to a self-consistent theory from the Planck scale to the onset of slow roll inflation, covering some 11 orders of magnitude in energy density and curvature. This preinflationary dynamics also opens a small window for novel effects, e.g., a source for non-Gaussianities, which could extend the reach of cosmological observations to the deep Planck regime of the early Universe.
Physical Review Letters, 1998
A `black hole sector' of non-perturbative canonical quantum gravity is introduced. The quantum bl... more A `black hole sector' of non-perturbative canonical quantum gravity is introduced. The quantum black hole degrees of freedom are shown to be described by a Chern-Simons field theory on the horizon. It is shown that the entropy of a large non-rotating black hole is proportional to its horizon area. The constant of proportionality depends upon the Immirzi parameter, which fixes the spectrum of the area operator in loop quantum gravity; an appropriate choice of this parameter gives the Bekenstein-Hawking formula S = A/4*l_p^2. With the same choice of the Immirzi parameter, this result also holds for black holes carrying electric or dilatonic charge, which are not necessarily near extremal.
Classical and Quantum Gravity, 2003
The isolated horizon framework is extended to include non-minimally coupled scalar fields. As exp... more The isolated horizon framework is extended to include non-minimally coupled scalar fields. As expected from the analysis based on Killing horizons, entropy is no longer given just by (a quarter of) the horizon area but also depends on the scalar field. In a subsequent paper these results will serve as a point of departure for a statistical mechanical derivation of entropy using quantum geometry.
Over the past three decades, black holes have played an important role in quantum gravity, mathem... more 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
A functional calculus on the space of (generalized) connections was recently introduced without a... more A functional calculus on the space of (generalized) connections was recently introduced without any reference to a background metric. It is used to continue the exploration of the quantum Riemannian geometry. Operators corresponding to volume of three-dimensional regions are regularized rigorously. It is shown that there are two natural regularization schemes, each of which leads to a well-defined operator. Both
Using the earlier developed classical Hamiltonian framework as the point of departure, we carry o... more Using the earlier developed classical Hamiltonian framework as the point of departure, we carry out a non-perturbative quantization of the sector of general relativity, coupled to matter, admitting non-rotating isolated horizons as inner boundaries. The emphasis is on the quantum geometry of the horizon. Polymer excitations of the bulk quantum geometry pierce the horizon endowing it with area. The intrinsic
Advances in Theoretical and Mathematical Physics, 2003
Applications of Riemannian quantum geometry to cosmology have had notable successes. In particula... more Applications of Riemannian quantum geometry to cosmology have had notable successes. In particular, the fundamental discreteness underlying quantum geometry has led to a natural resolution of the big bang singularity. However, the precise mathematical structure underlying loop quantum cosmology and the sense in which it implements the full quantization program in a symmetry reduced model has not been made explicit.
A new functional calculus, developed recently for a fully non- perturbative treatment of quantum ... more A new functional calculus, developed recently for a fully non- perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corre- sponding to areas of 2-surfaces are introduced and shown to be self-adjoint on the underlying (kinematical) Hilbert space of states. It is shown that their spectra are purely discrete
Journal of Physics Conference Series
The era of precision cosmology has allowed us to accurately determine many important cosmological... more The era of precision cosmology has allowed us to accurately determine many important cosmological parameters, in particular via the CMB. Confronting Loop Quantum Cosmology with these observations provides us with a powerful test of the theory. For this to be possible we need a detailed understanding of the generation and evolution of inhomogeneous perturbations during the early, Quantum Gravity, phase of the universe. Here we describe how Loop Quantum Cosmology provides a completion of the inflationary paradigm, that is consistent with the observed power spectra of the CMB.
Classical and Quantum Gravity, 2005
Equilibrium states of black holes can be modelled by isolated horizons. If the intrinsic geometry... more Equilibrium states of black holes can be modelled by isolated horizons. If the intrinsic geometry is spherical, they are called type I while if it is axi-symmetric, they are called type II. The detailed theory of the geometry of quantum type I horizons and the calculation of their entropy can be generalized to type II, thereby including arbitrary distortions and
Classical and Quantum Gravity, 2008
We consider four-dimensional spacetimes which are asymptotically flat at spatial infinity and sho... more We consider four-dimensional spacetimes which are asymptotically flat at spatial infinity and show that, in the first-order framework, the action principle for general relativity is well defined without the need of infinite counter terms. It naturally leads to a covariant phase space in which the Hamiltonians generating asymptotic symmetries provide the total energy momentum and angular momentum of the spacetime.
Classical and Quantum Gravity, 2004
To every axi-symmetric isolated horizon we associate two sets of numbers, Mn and Jn with n = 0, 1... more To every axi-symmetric isolated horizon we associate two sets of numbers, Mn and Jn with n = 0, 1, 2, ..., representing its mass and angular momentum multipoles. They provide a diffeomorphism invariant characterization of the horizon geometry. Physically, they can be thought of as the 'source multipoles' of black holes in equilibrium. These structures have a variety of potential
Physical Review D, 1997
The asymptotic behavior of Einstein-Rosen waves at null infinity in 4 dimensions is investigated ... more The asymptotic behavior of Einstein-Rosen waves at null infinity in 4 dimensions is investigated in {\it all} directions by exploiting the relation between the 4-dimensional space-time and the 3-dimensional symmetry reduction thereof. Somewhat surprisingly, the behavior in a generic direction is {\it better} than that in directions orthogonal to the symmetry axis. The geometric origin of this difference can be
Physical Review D, 1997
Gravitational waves with a space-translation Killing field are considered. In this case, the 4-di... more Gravitational waves with a space-translation Killing field are considered. In this case, the 4-dimensional Einstein vacuum equations are equivalent to the 3-dimensional Einstein equations with certain matter sources. This interplay between 4- and 3- dimensional general relativity can be exploited effectively to analyze issues pertaining to 4 dimensions in terms of the 3-dimensional structures. An example is provided by the
International Journal of Modern Physics D, 2001
Lecture Notes in Physics, 1982
Physical Review Letters, 2012
Since the standard inflationary paradigm is based on quantum field theory on classical space-time... more Since the standard inflationary paradigm is based on quantum field theory on classical space-times, it excludes the Planck era. Using techniques from loop quantum gravity, the paradigm is extended to a self-consistent theory from the Planck scale to the onset of slow roll inflation, covering some 11 orders of magnitude in energy density and curvature. This preinflationary dynamics also opens a small window for novel effects, e.g., a source for non-Gaussianities, which could extend the reach of cosmological observations to the deep Planck regime of the early Universe.
Physical Review Letters, 1998
A `black hole sector' of non-perturbative canonical quantum gravity is introduced. The quantum bl... more A `black hole sector' of non-perturbative canonical quantum gravity is introduced. The quantum black hole degrees of freedom are shown to be described by a Chern-Simons field theory on the horizon. It is shown that the entropy of a large non-rotating black hole is proportional to its horizon area. The constant of proportionality depends upon the Immirzi parameter, which fixes the spectrum of the area operator in loop quantum gravity; an appropriate choice of this parameter gives the Bekenstein-Hawking formula S = A/4*l_p^2. With the same choice of the Immirzi parameter, this result also holds for black holes carrying electric or dilatonic charge, which are not necessarily near extremal.
Classical and Quantum Gravity, 2003
The isolated horizon framework is extended to include non-minimally coupled scalar fields. As exp... more The isolated horizon framework is extended to include non-minimally coupled scalar fields. As expected from the analysis based on Killing horizons, entropy is no longer given just by (a quarter of) the horizon area but also depends on the scalar field. In a subsequent paper these results will serve as a point of departure for a statistical mechanical derivation of entropy using quantum geometry.
Over the past three decades, black holes have played an important role in quantum gravity, mathem... more 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
A functional calculus on the space of (generalized) connections was recently introduced without a... more A functional calculus on the space of (generalized) connections was recently introduced without any reference to a background metric. It is used to continue the exploration of the quantum Riemannian geometry. Operators corresponding to volume of three-dimensional regions are regularized rigorously. It is shown that there are two natural regularization schemes, each of which leads to a well-defined operator. Both
Using the earlier developed classical Hamiltonian framework as the point of departure, we carry o... more Using the earlier developed classical Hamiltonian framework as the point of departure, we carry out a non-perturbative quantization of the sector of general relativity, coupled to matter, admitting non-rotating isolated horizons as inner boundaries. The emphasis is on the quantum geometry of the horizon. Polymer excitations of the bulk quantum geometry pierce the horizon endowing it with area. The intrinsic
Advances in Theoretical and Mathematical Physics, 2003
Applications of Riemannian quantum geometry to cosmology have had notable successes. In particula... more Applications of Riemannian quantum geometry to cosmology have had notable successes. In particular, the fundamental discreteness underlying quantum geometry has led to a natural resolution of the big bang singularity. However, the precise mathematical structure underlying loop quantum cosmology and the sense in which it implements the full quantization program in a symmetry reduced model has not been made explicit.
A new functional calculus, developed recently for a fully non- perturbative treatment of quantum ... more A new functional calculus, developed recently for a fully non- perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corre- sponding to areas of 2-surfaces are introduced and shown to be self-adjoint on the underlying (kinematical) Hilbert space of states. It is shown that their spectra are purely discrete
Journal of Physics Conference Series
The era of precision cosmology has allowed us to accurately determine many important cosmological... more The era of precision cosmology has allowed us to accurately determine many important cosmological parameters, in particular via the CMB. Confronting Loop Quantum Cosmology with these observations provides us with a powerful test of the theory. For this to be possible we need a detailed understanding of the generation and evolution of inhomogeneous perturbations during the early, Quantum Gravity, phase of the universe. Here we describe how Loop Quantum Cosmology provides a completion of the inflationary paradigm, that is consistent with the observed power spectra of the CMB.
Classical and Quantum Gravity, 2005
Equilibrium states of black holes can be modelled by isolated horizons. If the intrinsic geometry... more Equilibrium states of black holes can be modelled by isolated horizons. If the intrinsic geometry is spherical, they are called type I while if it is axi-symmetric, they are called type II. The detailed theory of the geometry of quantum type I horizons and the calculation of their entropy can be generalized to type II, thereby including arbitrary distortions and
Classical and Quantum Gravity, 2008
We consider four-dimensional spacetimes which are asymptotically flat at spatial infinity and sho... more We consider four-dimensional spacetimes which are asymptotically flat at spatial infinity and show that, in the first-order framework, the action principle for general relativity is well defined without the need of infinite counter terms. It naturally leads to a covariant phase space in which the Hamiltonians generating asymptotic symmetries provide the total energy momentum and angular momentum of the spacetime.
Classical and Quantum Gravity, 2004
To every axi-symmetric isolated horizon we associate two sets of numbers, Mn and Jn with n = 0, 1... more To every axi-symmetric isolated horizon we associate two sets of numbers, Mn and Jn with n = 0, 1, 2, ..., representing its mass and angular momentum multipoles. They provide a diffeomorphism invariant characterization of the horizon geometry. Physically, they can be thought of as the 'source multipoles' of black holes in equilibrium. These structures have a variety of potential
Physical Review D, 1997
The asymptotic behavior of Einstein-Rosen waves at null infinity in 4 dimensions is investigated ... more The asymptotic behavior of Einstein-Rosen waves at null infinity in 4 dimensions is investigated in {\it all} directions by exploiting the relation between the 4-dimensional space-time and the 3-dimensional symmetry reduction thereof. Somewhat surprisingly, the behavior in a generic direction is {\it better} than that in directions orthogonal to the symmetry axis. The geometric origin of this difference can be
Physical Review D, 1997
Gravitational waves with a space-translation Killing field are considered. In this case, the 4-di... more Gravitational waves with a space-translation Killing field are considered. In this case, the 4-dimensional Einstein vacuum equations are equivalent to the 3-dimensional Einstein equations with certain matter sources. This interplay between 4- and 3- dimensional general relativity can be exploited effectively to analyze issues pertaining to 4 dimensions in terms of the 3-dimensional structures. An example is provided by the
International Journal of Modern Physics D, 2001
Lecture Notes in Physics, 1982