110 research outputs found
Ehrenfest's Principle and the Problem of Time in Quantum Gravity
We elaborate on a proposal made by Greensite and others to solve the problem
of time in quantum gravity. The proposal states that a viable concept of time
and a sensible inner product can be found from the demand for the Ehrenfest
equations to hold in quantum gravity. We derive and discuss in detail exact
consistency conditions from both Ehrenfest equations as well as from the
semiclassical approximation. We also discuss consistency conditions arising
from the full field theory. We find that only a very restricted class of
solutions to the Wheeler-DeWitt equation fulfills all consistency conditions.
We conclude that therefore this proposal must either be abandoned as a means to
solve the problem of time or, alternatively, be used as an additional boundary
condition to select physical solutions from the Wheeler-DeWitt equation.Comment: 20 pages, LATE
Semiclassical quantum states for black holes
I discuss the semiclassical approximation for the Wheeler-DeWitt equation
when applied to the CGHS model and spherically symmetric gravity. Special
attention is devoted to the issues of Hawking radiation, decoherence of
semiclassical states, and black hole entropy.Comment: 8 pages, LATEX, contribution for the Second Conference on Constrained
Dynamics and Quantum Gravity, Santa Margherita, Italy, September 199
Canonical Quantization of Spherically Symmetric Dust Collapse
Quantum gravity effects are likely to play a crucial role in determining the
outcome of gravitational collapse during its final stages. In this contribution
we will outline a canonical quantization of the LeMaitre-Tolman-Bondi models,
which describe the collapse of spherical, inhomogeneous, non-rotating dust.
Although there are many models of gravitational collapse, this particular class
of models stands out for its simplicity and the fact that both black holes and
naked singularity end states may be realized on the classical level, depending
on the initial conditions. We will obtain the appropriate Wheeler-DeWitt
equation and then solve it exactly, after regularization on a spatial lattice.
The solutions describe Hawking radiation and provide an elegant microcanonical
description of black hole entropy, but they raise other questions, most
importantly concerning the nature of gravity's fundamental degrees of freedom.Comment: 19 pages no figures. Contribution to a festschrift in honor of Joshua
N. Goldber
Quantum general relativity and Hawking radiation
In a previous paper we have set up the Wheeler-DeWitt equation which
describes the quantum general relativistic collapse of a spherical dust cloud.
In the present paper we specialize this equation to the case of matter
perturbations around a black hole, and show that in the WKB approximation, the
wave-functional describes an eternal black hole in equilibrium with a thermal
bath at Hawking temperature.Comment: 13 pages, minor revisions in: (i) para 5 of Introduction, (ii) para
following Eqn. (10). Revised version to appear in Phys. Rev.
Microcanonical statistics of black holes and bootstrap condition
The microcanonical statistics of the Schwarzschild black holes as well as the
Reissner-Nordstrm black holes are analyzed. In both cases we set
up the inequalities in the microcanonical density of states.
These are then used to show that the most probable configuration in the gases
of black holes is that one black hole acquires all of the mass and all of the
charge at high energy limit. Thus the black holes obey the statistical
bootstrap condition and, in contrast to the other investigation, we see that
U(1) charge does not break the bootstrap property.Comment: 16 pages. late
A Quantum Mechanical Model of the Reissner-Nordstrom Black Hole
We consider a Hamiltonian quantum theory of spherically symmetric,
asymptotically flat electrovacuum spacetimes. The physical phase space of such
spacetimes is spanned by the mass and the charge parameters and of the
Reissner-Nordstr\"{o}m black hole, together with the corresponding canonical
momenta. In this four-dimensional phase space, we perform a canonical
transformation such that the resulting configuration variables describe the
dynamical properties of Reissner-Nordstr\"{o}m black holes in a natural manner.
The classical Hamiltonian written in terms of these variables and their
conjugate momenta is replaced by the corresponding self-adjoint Hamiltonian
operator, and an eigenvalue equation for the ADM mass of the hole, from the
point of view of a distant observer at rest, is obtained. Our eigenvalue
equation implies that the ADM mass and the electric charge spectra of the hole
are discrete, and the mass spectrum is bounded below. Moreover, the spectrum of
the quantity is strictly positive when an appropriate self-adjoint
extension is chosen. The WKB analysis yields the result that the large
eigenvalues of the quantity are of the form , where
is an integer. It turns out that this result is closely related to
Bekenstein's proposal on the discrete horizon area spectrum of black holes.Comment: 37 pages, Plain TeX, no figure
Semiclassical Black Hole States and Entropy
We discuss semiclassical states in quantum gravity corresponding to
Schwarzschild as well as Reissner Nordstr\"om black holes. We show that reduced
quantisation of these models is equivalent to Wheeler-DeWitt quantisation with
a particular factor ordering. We then demonstrate how the entropy of black
holes can be consistently calculated from these states. While this leads to the
Bekenstein-Hawking entropy in the Schwarzschild and non-extreme
Reissner-Nordstr\"om cases, the entropy for the extreme Reissner-Nordstr\"om
case turns out to be zero.Comment: Revtex, 15 pages, some clarifying comments and additional references
included, to appear in Phys. Rev.
Topology Change in Canonical Quantum Cosmology
We develop the canonical quantization of a midisuperspace model which
contains, as a subspace, a minisuperspace constituted of a
Friedman-Lema\^{\i}tre-Robertson-Walker Universe filled with homogeneous scalar
and dust fields, where the sign of the intrinsic curvature of the spacelike
hypersurfaces of homogeneity is not specified, allowing the study of topology
change in these hypersurfaces. We solve the Wheeler-DeWitt equation of the
midisuperspace model restricted to this minisuperspace subspace in the
semi-classical approximation. Adopting the conditional probability
interpretation, we find that some of the solutions present change of topology
of the homogeneous hypersurfaces. However, this result depends crucially on the
interpretation we adopt: using the usual probabilistic interpretation, we find
selection rules which forbid some of these topology changes.Comment: 23 pages, LaTex file. We added in the conclusion some comments about
path integral formalism and corrected litle misprinting
Must Quantum Spacetimes Be Euclidean?
The Bohm-de Broglie interpretation of quantum mechanics is applied to
canonical quantum cosmology. It is shown that, irrespective of any
regularization or choice of factor ordering of the Wheeler-DeWitt equation, the
unique relevant quantum effect which does not break spacetime is the change of
its signature from lorentzian to euclidean. The other quantum effects are
either trivial or break the four-geometry of spacetime. A Bohm-de Broglie
picture of a quantum geometrodynamics is constructed, which allows the
investigation of these latter structures. For instance, it is shown that any
real solution of the Wheeler-De Witt equation yields a generate four-geometry
compatible with the strong gravity limit of General Relativity and the Carroll
group. Due to the more detailed description of quantum geometrodynamics given
by the Bohm-de Broglie interpretation, some new boundary conditions on
solutions of the Wheeler-DeWitt equation must be imposed in order to preserve
consistency of this finer view.Comment: 42 pages LaTeX, last version with minor corrections, being the most
importants on pages 0, 6, 11, 21, 23, and 30 . The new title does not change
our conclusion
The Bohm Interpretation of Quantum Cosmology
I make a review on the aplications of the Bohm-De Broglie interpretation of
quantum mechanics to quantum cosmology. In the framework of minisuperspaces
models, I show how quantum cosmological effects in Bohm's view can avoid the
initial singularity, isotropize the Universe, and even be a cause for the
present observed acceleration of the Universe. In the general case, we
enumerate the possible structures of quantum space and time.Comment: 28 pages, 1 figure, contribution to the James Cushing festschrift to
appear in Foundations of Physic
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