arXiv subjects

Cenalo Vaz

Publications and source records attributed to Cenalo Vaz.

At least 55 records · Page 3Linked to original sources

arXiv2002

Dark Radiation and Localization of Gravity on the Brane

We discuss the dynamics of a spherically symmetric dark radiation vaccum in the Randall-Sundrum brane world scenario. Under certain natural assumptions we show that the Einstein equations on the brane form a closed system. For a de Sitter brane we determine exact dynamical and inhomogeneous solutions which depend on the brane cosmological constant, on the dark radiation tidal charge and on its initial configuration. We define the conditions leading to singular or globally regular solutions. We also analyse the localization of gravity near the brane and show that a phase transition to a regime where gravity propagates away from the brane may occur at short distances during the collapse of positive dark energy density.

hep-th↗

arXiv2002

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.

gr-qc↗

arXiv2002

Dark Radiation Dynamics on the Brane

We investigate the dynamics of a spherically symmetric vaccum 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.

hep-th↗

arXiv2002

Toward a Quantization of Null Dust Collapse

Spherically symmetric, null dust clouds, like their time-like counterparts, may collapse classically into black holes or naked singularities depending on their initial conditions. We consider the Hamiltonian dynamics of the collapse of an arbitrary distribution of null dust, expressed in terms of the physical radius, $R$, the null coordinates, $V$ for a collapsing cloud or $U$ for an expanding cloud, the mass function, $m$, of the null matter, and their conjugate momenta. This description is obtained from the ADM description by a Kuchař-type canonical transformation. The constraints are linear in the canonical momenta and Dirac's constraint quantization program is implemented. Explicit solutions the constraints are obtained for both expanding and contracting null dust clouds with arbitrary mass functions.

gr-qc↗

arXiv2001

Quantum Black Holes from Quantum Collapse

The Schwarzschild black hole can be viewed as the special case of the marginally bound Lema\^ıtre-Tolman-Bondi models of dust collapse which corresponds to a constant mass function. We have presented a midi-superspace quantization of this model for an arbitrary mass-function in a separate publication. In this communication we show that our solution leads both to Bekenstein's area spectrum for black holes as well as to the black hole entropy, which, in this context, is naturally interpreted as the loss of information of the original matter distribution within the collapsing dust cloud.

gr-qc↗

arXiv2001

Naked singularities and quantum gravity

There are known models of spherical gravitational collapse in which the collapse ends in a naked shell-focusing singularity for some initial data. If a massless scalar field is quantized on the classical background provided by such a star, it is found that the outgoing quantum flux of the scalar field diverges in the approach to the Cauchy horizon. We argue that the semiclassical approximation (i.e. quantum field theory on a classical curved background) used in these analyses ceases to be valid about one Planck time before the epoch of naked singularity formation, because by then the curvature in the central region of the star reaches Planck scale. It is shown that during the epoch in which the semiclassical approximation is valid, the total emitted energy is about one Planck unit, and is not divergent. We also argue that back reaction in this model does not become important so long as gravity can be treated classically. It follows that the further evolution of the star will be determined by quantum gravitational effects, and without invoking quantum gravity it is not possible to say whether the star radiates away on a short time scale or settles down into a black hole state.

gr-qc↗

arXiv2001

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

LeMa\^ıtre-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\^ıtre-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, $τ$, and the mass function, $F$, are the canonical coordinates, $R(r)$, $τ(r)$ 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.

gr-qc↗

arXiv2000

The Quantum States and the Statistical Entropy of the Charged Black Hole

We quantize the Reissner-Nordström black hole using an adaptation of Kuchař's canonical decomposition of the Kruskal extension of the Schwarzschild black hole. The Wheeler-DeWitt equation turns into a functional Schroedinger equation in Gaussian time by coupling the gravitational field to a reference fluid or dust. The physical phase space of the theory is spanned by the mass, $M$, the charge, $Q$, the physical radius, $R$, the dust proper time, $τ$, and their canonical momenta. The exact solutions of the functional Schroedinger equation imply that the difference in the areas of the outer and inner horizons is quantized in integer units. This agrees in spirit, but not precisely, with Bekenstein's proposal on the discrete horizon area spectrum of black holes. We also compute the entropy in the microcanonical ensemble and show that the entropy of the Reissner-Nordström black hole is proportional to this quantized difference in horizon areas.

gr-qc↗

arXiv2000

Radiation flux and spectrum in the Vaidya collapse model

We consider the quantization of a massless scalar field, using the geometric optics approximation, in the background spacetime of a collapsing spherical self-similar Vaidya star, which forms a black hole or a naked singularity. We show that the outgoing radiation flux of the quantized scalar field diverges on the Cauchy horizon. The spectrum of the produced scalar partcles is non-thermal when the background develops a naked singularity. These results are analogous to those obtained for the scalar quantization on a self-similar dust cloud.

gr-qc↗

arXiv2000

Divergence of the Quantum Stress Tensor on the Cauchy Horizon in 2-d Dust Collapse

We prove that the quantum stress tensor for a massless scalar field in two dimensional non-selfsimilar Tolman Bondi dust collapse and Vaidya radiation collapse models diverges on the Cauchy horizon, if the latter exists. The two dimensional model is obtained by suppressing angular co-ordinates in the corresponding four dimensional spherical model.

gr-qc↗

arXiv1999

Quantum Radiation from Black Holes and Naked Singularities in Spherical Dust Collapse

A sufficiently massive collapsing star will end its life as a spacetime singularity. The nature of the Hawking radiation emitted during collapse depends critically on whether the star's boundary conditions are such as would lead to the eventual formation of a black hole or, alternatively, to the formation of a naked singularity. This latter possibility is not excluded by the singularity theorems. We discuss the nature of the Hawking radiation emitted in each case. We justify the use of Bogoliubov transforms in the presence of a Cauchy horizon and show that if spacetime is assumed to terminate at the Cauchy horizon, the resulting spectrum is thermal, but with a temperature different from the Hawking temperature.

gr-qc↗

arXiv1999

Canonical Quantization and the Statistical Entropy of the Schwarzschild Black Hole

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, $M \sim \sqrt{\cal N} M_p$, where ${\cal N} \in {\bf N}$. From the microcanonical ensemble, we derive the statistical entropy of the black hole by explicitly counting the microstates corresponding to a macrostate of fixed total energy.

gr-qc↗

arXiv1999

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.

gr-qc↗

arXiv1998

Mass Quantization of the Schwarzschild Black Hole

We examine the Wheeler-DeWitt equaton for a static, eternal Schwarzschild black hole in Kucha\v r-Brown variables and obtain its energy eigenstates. Consistent solutions vanish in the exterior of the Kruskal manifold and are non-vanishing 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 (ADM) mass of the black hole according to a relation conjectured long ago by Bekenstein, $M \sim \sqrt{n}M_p$. 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.

gr-qc↗

arXiv1998

On the Spectrum of the Radiation from a Naked Singularitry

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 $T = (8πM)^{-1}$. 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.

gr-qc↗

arXiv1998

Particle Creation in the Marginally Bound, Self Similar Collapse of Inhomogeneous Dust

We consider the evaporation of the (shell focusing) naked singularity formed during the self-similar collapse of a marginally bound inhomogeneous dust cloud, in the geometric optics approximation. We show that, neglecting the back reaction of the spacetime, the radiation on $\scrip$ tends to infinity as the Cauchy Horizon is approached. Two consequences can be expected from this result: (a) that the back reaction of spacetime will be large and eventually halt the formation of a naked singularity thus preserving the Cosmic Censorship Hypothesis and (b) matter attempting to collapse into a naked singularity will radiate away energy at an intense rate, thereby possibly providing experimental signatures of quantum effects in curved spacetimes.

gr-qc↗

arXiv1998

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.

gr-qc↗

arXiv1996

Quantum Naked Singularities in 2d Dilaton Gravity

Roughly speaking, naked singularities are singularities that may be seen by timelike observers. The Cosmic Censorship conjecture forbids their existence by stating that a reasonable system of energy will not, under reasonable conditions, collapse into a naked singularity. There are however many (classical) counter-examples to this conjecture in the literature. We propose a defense of the conjecture through the quantum theory. We will show that the Hawking effect and the accompanying back reaction, when consistently applied to naked singularities in two dimensional models of dilaton gravity with matter and a cosmological constant, prevent their formation by causing them to explode or emit radiation catastrophically. This contrasts with black holes which radiate slowly. If this phenomenon is reproduced in the four dimensional world, the explosion of naked singularities should have observable consequences.

hep-th↗