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.
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.
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.
24124943
Toward a quantization of null dust collapse
Spherically symmetric, null dust clouds, like their timelike 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 Arnowitt-Deser-Misner description by a Kucha\ifmmode \check{r}\else \v{r}\fi{}-type canonical transformation. The constraints are linear in the canonical momenta and Dirac's constraint quantization program is implemented. Explicit solutions to the constraints are obtained for both expanding and contracting null dust clouds with arbitrary mass functions.
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.
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.
117803800
Tolman's solutions in higher dimensional space-time.
123030808
Field of a charged particle in general scalar-tensor theory
The field equations in the general scalar-tensor theory of gravitation proposed by Bergmann, Wagoner, and Nordtvedt are studied for a charged static and spherically symmetric vacuum field. Closed-form exact solutions of the field equations are presented for the scalar-tensor theories in the form due to Barker and Schwinger. The solutions may be considered as describing the field of a charged mass point surrounded by a scalar-tensor field.
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.
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.
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.