7721855
Gamma-Ray Bursts and Quantum Cosmic Censorship
Gamma-ray bursts are believed to result from the coalescence of binary neutron stars. However, the standard proposals for conversion of the gravitational energy to thermal energy have difficulties. We show that if the merger of the two neutron stars results in a naked singularity, instead of a black hole, the ensuing quantum particle creation can provide the requisite thermal energy in a straightforward way. The back-reaction of the created particles can avoid the formation of the naked singularity predicted by the classical theory. Hence cosmic censorship holds in the quantum theory, even if it were to be violated in classical general relativity.
16490636
The final fate of spherical inhomogeneous dust collapse
We examine, in a general manner, the role played by the initial density and velocity distributions in the gravitational collapse of a spherically symmetric inhomogeneous dust cloud. Such a collapse is described by the Tolman - Bondi metric which has two free functions: the `mass function' and the `energy function', which are determined by the initial density and velocity profiles of the cloud. The collapse can end in either a black hole or a naked singularity, depending on the initial parameters characterizing these profiles. In the marginally bound case, we find that the collapse ends in a naked singularity if the leading non-vanishing derivative of the density at the centre is either the first one or the second one. If the first two derivatives are zero, and the third derivative non-zero, the singularity could either be naked or covered, depending on a quantity determined by the third derivative and the central density. If the first three derivatives are zero, the collapse ends in a black hole. In particular, the classic result of Oppenheimer and Snyder, that homogeneous dust collapse leads to a black hole, is recovered as a special case. Analogous results are found when the cloud is not marginally bound, and also for the case of a cloud starting from rest. A condition on the initial density profile is given for the singularity to be globally naked. We also show how the strength of the naked singularity depends on the density and velocity distribution. Our analysis generalizes and simplifies the earlier works of Christodoulou and Newman by dropping the assumption of evenness of density functions. It turns out that relaxing this assumption allows for a smooth transition from the naked singularity phase to the black hole phase, and also allows for the occurrence of strong curvature naked singularities.
27984646
Quantum general relativity and Hawking radiation
In a previous paper we 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.
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.
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.
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.
122267670
Some static solutions in the general scalar‐tensor theory
Exact solutions are found for the static gravitational fields for a matter‐free space in the general scalar‐tensor theory of Nordtvedt–Barker–Schwinger. The singular behavior of some of the invariants has also been discussed for the solutions in Barker and Schwinger theories.
121240575
Stationary Universe in General Relativity and Lyra's Geometry
The stationary universe solutions have been studied using the metrics of VAN Stockum (1937) and Godel (1949) in a New ST theory (Saez and Ballester, 1985), general relativity with variable cosmological term (Narlikar et al., 1991), Lyra's geometry (Sen, 1957) and Cosmic strings. It has been shown that the stationary universe has rigid rotation in ST theory. In the presence of variable cosmological term, there is non-rigid rotation in the presence of Zeldovich fluid for van Stockum metric. In Lyra's geometry the only solution is possible when the gauge function β is variable and there is Zeldovich fluid. However, in the presence of cosmic strings, there is no solution with van Stockum or Godel metrics.
116059635
Viscous cosmological models with particle creation in Brans-Dicke theory
The effect of bulk viscosity on the evolution of the spatially flat Friedmann-Robertson-Walker models in the context of open thermodynamical systems, which allow particle creation, is analyzed within the framework of Brans-Dicke theory. Particle creation and bulk viscosity have been considered as separated irreversible processes. To accommodate the viscous pressure and creation pressure, which is associated with creation of matter out of gravitational field, the energy-momentum tensor is modified. Dynamical behaviour of the models have been discussed.
120934994
Bianchi type- I, III, V, VIo and Kantowski-Sachs models in scalar-tensor theories with dynamic cosmological constant
The effect of a time-dependent cosmological constant is considered in a family of scalar-tensor theories. The Bianchi type I, III, V, VIo and Kantowski-Sachs models for vacuum and perfect fluid matter are found. The gravitational constant decreases with time so that these models satisfy the Dirac hypothesis. The “cosmological constant” also decreases with time, therefore it can have a very small value at the present time.