119218867
Quantum Gravitational Collapse and Hawking Radiation in 2+1 Dimensions
We develop the canonical theory of gravitational collapse in $2+1$ dimensions with a negative cosmological constant and obtain exact solutions of the Wheeler-DeWitt equation regularized on a lattice. We employ these solutions to derive the Hawking radiation from black holes formed in all models of dust collapse. We obtain an (approximate) Planck spectrum near the horizon characterized by the Hawking temperature ${T}_{\mathrm{H}}=\ensuremath{\hbar}\sqrt{G\ensuremath{\Lambda}M}/2\ensuremath{\pi}$, where $M$ is the mass of a black hole that is presumed to form at the center of the collapsing matter cloud and $\ensuremath{-}\ensuremath{\Lambda}$ is the cosmological constant. Our solutions to the Wheeler-DeWitt equation are exact, so we are able to reliably compute the gray-body factors that result from going beyond the near-horizon region.
118510273
THE CONNECTION BETWEEN "EMERGENCE OF TIME FROM QUANTUM GRAVITY" AND "DYNAMICAL COLLAPSE OF THE WAVE FUNCTION IN QUANTUM MECHANICS"
There are various reasons to believe that quantum theory could be an emergent phenomenon. Trace dynamics is an underlying classical dynamics of noncommuting matrices, from which quantum theory and classical mechanics have been shown to emerge, in the thermodynamic approximation. However, the time that is used to describe evolution in quantum theory is an external classical time, and is in turn expected to be an emergent feature — a relic of an underlying theory of quantum gravity. In this essay we borrow ideas from trace dynamics to show that classical time is a thermodynamic approximation to an operator time in quantum gravitational physics. This prediction will be put to test by ongoing laboratory experiments attempting to construct superposed states of macroscopic objects.
119086760
Comparing quantum black holes and naked singularities
There are models of gravitational collapse in classical general relativity which admit the formation of naked singularities as well as black holes. These include fluid models as well as models with scalar fields as matter. Even if fluid models were to be regarded as unphysical in their matter content, the remaining class of models (based on scalar fields) generically admit the formation of visible regions of finite but arbitrarily high curvature. Hence it is of interest to ask, from the point of view of astrophysics, as to what a stellar collapse leading to a naked singularity (or to a visible region of very high curvature) will look like, to a far away observer. The emission of energy during such a process may be divided into three phases - (i) the classical phase, during which matter and gravity can both be treated according to the laws of classical physics, (ii) the semiclassical phase, when gravity is treated classically but matter behaves as a quantum field, and (iii) the quantum gravitational phase. In this review, we first give a summary of the status of naked singularities in classical relativity, and then report some recent results comparing the semiclassical phase of black holes with the semiclassical phase of spherical collapse leading to a naked singularity. In particular, we ask how the quantum particle creation during the collapse leading to a naked singularity compares with the Hawking radiation from a star collapsing to form a black hole. It turns out that there is a fundamental difference between the two cases. A spherical naked star emits only about one Planck energy during its semiclassical phase, and the further evolution can only be determined by the laws of quantum gravity. This contrasts with the semiclassical evaporation of a black hole.
16349342
A characterization of the central shell-focusing singularity in spherical gravitational collapse
We give a characterization of the central shell-focusing curvature singularity that can form in the spherical gravitational collapse of a bound matter distribution obeying the dominant energy condition. This characterization is based on the limiting behaviour of the mass function in the neighbourhood of the singularity. Depending on the rate of growth of the mass as a function of the area radius R, the singularity may be either covered or naked. The singularity is naked if this growth rate is slower than R, covered if it is faster than R, and either naked or covered if the growth rate is the same as R.
1570088
Radiation flux and spectrum in the Vaidya collapse model
Abstract 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.
118799695
The three and a half layers of dynamics : analog, digital, semi-digital, analog
Quantum theory is extremely successful in explaining most physical phenomena, and is not contradicted by any experiment. Yet, the theory has many puzzling features : the occurrence of probabilities, the unclear distinction between the microscopic and the macroscopic, the unexplained absence of superpositions in positions of macroscopic objects, the dependence of the theory on an external classical time, and the experimentally verified but peculiar `influence' outside the light-cone in EPR experiments. These puzzles point towards a conflict between quantum theory and our present understanding of spacetime structure, and suggest the existence of a deeper theory. In this essay we make the case that in the underlying theory the matter and spacetime degrees of freedom are non-commuting matrices, and yet the dynamics is analog. A digital quantum-theory like dynamics for matter as well as spacetime emerges in the statistical thermodynamic approximation to this deeper theory. When most of the matter clumps into macroscopic structures, it is shown to behave classically, and it induces classical dynamics on spacetime; this is the eventual analog limit, our macroscopic world. In between the digital layer and the uppermost analog layer is the realm of standard quantum theory - microscopic objects and their interaction with measuring apparatuses on a classical spacetime background : the semi-digital approximation. Such a multi-layered description of dynamics can explain the puzzling features of quantum theory, and is testable by ongoing laboratory experiments.
121368055
GENERAL CLASS OF SCALAR-TENSOR THEORIES: A REVIEW
The general class of scalar-tensor theories is discussed in which, in contrast to Brans-Dicke theory, the coupling parameter ω is not a constant but a function of the scalar field ϕ. Some other generalizations of the Brans-Dicke theory have also been discussed in brief. The physical aspects of these theories have been dealt. The cosmological models in scalar-tensor theories have been discussed in detail. Finally some open problems in these theories have been pointed out.
117011561
On exact static spherically symmetric solutions in general relativity, Einstein-Cartan theory and higher-dimensional theories
The equations describing the hydrostatic equilibrium of a static general relativistic fluid sphere are obtained for magnetofluids, Einstein-Cartan theory and anisotropic fluids in four dimensions and perfect fluids in D (D ≥ 4) dimensions. The method due to Hojman and Santamarina and Berger et al. is used to obtain a new and larger class of solutions. Illustrative examples have been given which lead to generalization of the Schwarschild exterior solution and the relativistic models for spiral galaxies and dense stars (Hojman et al.).
117803800
Tolman's solutions in higher dimensional space-time.
116888804
Bianchi type V and VI0 cosmological models in Lyra geometry
The Bianchi type V and VI0 models have been investigated in Lyra geometry in both the cases with the gauge function β is a time dependent and β=constant. The physical behaviour of these models has been discussed.
121342410
Bianchi type-V cosmological models with perfect fluid and dark energy
We consider a self-consistent system of Bianchi type-V cosmology and binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be one obeying the usual equation of state p=γρ with γ∈[0,1]. The dark energy is considered to be either the quintessence or Chaplygin gas. Exact solutions to the corresponding Einstein equations are obtained as a quadrature. The cases of disordered radiation and models with power-law and exponential expansion have discussed in detail. For large t, the models tend to be isotropic.