Cenalo Vaz

Mass quantization of the Schwarzschild black hole

We examine the Wheeler-DeWitt equation for a static, eternal Schwarzschild black hole in Kucha{hacek r}-Brown variables and obtain its energy eigenstates. Consistent solutions vanish in the exterior of the Kruskal manifold and are nonvanishing only in the interior. The system is reminiscent of a particle in a box. States of definite parity avoid the singular geometry by vanishing at the origin. These definite parity states admit a discrete energy spectrum, depending on one quantum number which determines the Arnowitt-Deser-Misner mass of the black hole according to a relation conjectured long ago by Bekenstein M{approximately}{radical} (n) M{sub p}. If attention is restricted only to these quantized energy states, a black hole is described not only by its mass but also by its parity. States of indefinite parity do not admit a quantized mass spectrum. {copyright} {ital 1999} {ital The American Physical Society}

Dark radiation dynamics on the brane

We investigate the dynamics of a spherically symmetric vacuum on a Randall and Sundrum 3-brane world. Under certain natural conditions, the effective Einstein equations on the brane form a closed system for spherically symmetric dark radiation. We determine exact dynamical and inhomogeneous solutions, which are shown to depend on the brane cosmological constant, on the dark radiation tidal charge and on its initial energy configuration. We identify the conditions defining these solutions as singular or as globally regular. Finally, we discuss the confinement of gravity to the vicinity of the brane and show that a phase transition to a regime where gravity is not bound to the brane may occur at short distances during the collapse of positive dark energy density on a realistic de Sitter brane.

Toward a midisuperspace quantization of LeMaitre-Tolman-Bondi collapse models

LeMaitre-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 semiclassically as quantum fluctuations of the gravitational field are expected to dominate before the final state is reached. We present a canonical reduction of LeMaitre-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. Diracs 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.

On the spectrum of the radiation from a naked singularity

Abstract In the final stages of collapse, quantum radiation due to particle creation from a naked singularity is expected to be significantly different from black hole radiation. In certain models of collapse it has been shown that, neglecting the back reaction of spacetime, the particle flux on future null infinity grows as the inverse square of the distance from the Cauchy horizon. This is to be contrasted with the flux of radiation from a black hole, which approaches a constant (inversely proportional to the square of its mass) in the neighborhood of its event horizon. The spectrum of black hole radiation is identical to that of a black body at temperature T =(8 πM ) −1 . We derive the radiation spectrum for a naked singularity formed in the collapse of a marginally bound inhomogeneous dust cloud and show that the spectrum is not black body and admits no simple interpretation.

Brane world dynamics and conformal bulk fields

In the Randall-Sundrum scenario we investigate the dynamics of a spherically symmetric 3-brane world when matter fields are present in the bulk. To analyze the 5-dimensional Einstein equations we employ a global conformal transformation whose factor characterizes the

Canonical quantization, conformal fields and the statistical entropy of the Schwarzschild black hole

Z_2

PARTICLE CREATION IN THE MARGINALLY BOUND, SELF-SIMILAR COLLAPSE OF INHOMOGENEOUS DUST

symmetric warp. We find a new set of exact dynamical collapse solutions which localize gravity in the vicinity of the brane for a stress-energy tensor of conformal weight -4 and a warp factor that depends only on the coordinate of the fifth dimension. Geometries which describe the dynamics of inhomogeneous dust and generalized dark radiation on the brane are shown to belong to this set. The conditions for singular or globally regular behavior and the static marginally bound limits are discussed for these examples. Also explicitly demonstrated is complete consistency with the effective point of view of a 4-dimensional observer who is confined to the brane and makes the same assumptions about the bulk degrees of freedom.

Quantum stress tensor in self-similar spherical dust collapse

The canonical quantization of a Schwarzschild black hole yields a picture of the black hole that is shown to be equivalent to a collection of oscillators whose density of levels is commensurate with that of the statistical bootstrap model. Energy eigenstates of definite parity exhibit the Bekenstein mass spectrum,

Wilson loops and black holes in (2+1)-dimensions

M \sim \sqrt{\cal N} M_p

A simple derivation of the naked singularity in spherical dust collapse

, where