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

Do Naked Singularities Form?

A naked singularity is formed by the collapse of a Sine-Gordon soliton in 1+1 dimensional dilaton gravity with a negative cosmological constant. We examine the quantum stress tensor resulting from the formation of the singularity. Consistent boundary conditions require that the incoming soliton is accompanied by a flux of incoming radiation across past null infinity, but neglecting the back reaction of the spacetime leads to the absurd conclusion that the total energy entering the system by the time the observer is able to receive information from the singularity is infinite. We conclude that the back reaction must prevent the formation of the naked singularity.Comment: 7 pages (21 Kb), PHYZZX. Revised version to appear in Class. & Quant. Grav. Letts. A discussion of the consistency of the Sine-Gordon model is include

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.

The Quantum Stress-Tensor in Self-Similar Spherical Dust Collapse

We calculate the quantum stress tensor for a massless scalar field in the 2-d self-similar spherical dust collapse model which admits a naked singularity. We find that the outgoing radiation flux diverges on the Cauchy horizon. This may have two consequences. The resultant back reaction may prevent the naked singularity from forming, thus preserving cosmic censorship through quantum effects. The divergent flux may lead to an observable signature differentiating naked singularities from black holes in astrophysical observations.Comment: Latex File, 19 page

A simple derivation of the naked singularity in spherical dust collapse

We describe a simple method of determining whether the singularity that forms in the spherically symmetric collapse of inhomogeneous dust is naked or covered. This derivation considerably simplifies the analysis given in the earlier literature, while giving the same results as have been obtained before.Comment: Latex, 9 page

Soliton Induced Singularities in 2 d Gravity and their Evaporation

Positive energy singularities induced by Sine-Gordon solitons in 1+1 dimensional dilaton gravity with positive and negative cosmological constant are considered. When the cosmological constant is positive, the singularities combine a white hole, a timelike singularity and a black hole joined smoothly near the soliton center. When the cosmological constant is negative, the solutions describe two timelike singularities joined smoothly near the soliton center. We describe these spacetimes and examine their evaporation in the one loop approximation.Comment: 15 pages (37.7 kb), PHYZZX. Figures available from authors

Black hole area quantization

It has been argued by several authors that the quantum mechanical spectrum of black hole horizon area must be discrete. This has been confirmed in different formalisms, using different approaches. Here we concentrate on two approaches, the one involving quantization on a reduced phase space of collective coordinates of a Black Hole and the algebraic approach of Bekenstein. We show that for non-rotating, neutral black holes in any spacetime dimension, the approaches are equivalent. We introduce a primary set of operators sufficient for expressing the dynamical variables of both, thus mapping the observables in the two formalisms onto each other. The mapping predicts a Planck size remnant for the black hole.Comment: 7 pages, uses MPLA style file (included). Revised version with changes in notation for clarity and consistency. To appear in MPL

Toward a Midisuperspace Quantization of LeMaitre-Tolman-Bondi Collapse Models

LeMa\^\i tre-Tolman-Bondi models of spherical dust collapse have been used and continue to be used extensively to study various stellar collapse scenarios. It is by now well-known that these models lead to the formation of black holes and naked singularities from regular initial data. The final outcome of the collapse, particularly in the event of naked singularity formation, depends very heavily on quantum effects during the final stages. These quantum effects cannot generally be treated semi-classically as quantum fluctuations of the gravitational field are expected to dominate before the final state is reached. We present a canonical reduction of LeMa\^\i tre-Tolman-Bondi space-times describing the marginally bound collapse of inhomogeneous dust, in which the physical radius, $R$, the proper time of the collapsing dust, $\tau$, and the mass function, $F$, are the canonical coordinates, $R(r)$, $\tau(r)$ and $F(r)$ on the phase space. Dirac's constraint quantization leads to a simple functional (Wheeler-DeWitt) equation. The equation is solved and the solution can be employed to study some of the effects of quantum gravity during gravitational collapse with different initial conditions.Comment: 9 pages, 1 figure, Latex file. Minor corrections made. A general solution of the constraints is presented. Revised version to appear in Phys. Rev.

Spherically symmetric scalar field collapse in any dimension

We describe a formalism and numerical approach for studying spherically symmetric scalar field collapse for arbitrary spacetime dimension d and cosmological constant Lambda. The presciption uses a double null formalism, and is based on field redefinitions first used to simplify the field equations in generic two-dimensional dilaton gravity. The formalism is used to construct code in which d and Lambda are input parameters. The code reproduces known results in d = 4 and d = 6 with Lambda = 0. We present new results for d = 5 with zero and negative Lambda.Comment: 16 pages, 6 figures, typos corrected, presentational changes, PRD in pres