17788970
Quantum mechanics without spacetime - a possible case for noncommutative differential geometry?
The rules of quantum mechanics require a time coordinate for their formulation. However, a notion of time is in general possible only when a classical spacetime geometry exists. Such a geometry is itself produced by classical matter sources. Thus it could be said that the currently known formulation of quantum mechanics pre-assumes the presence of classical matter fields. A more fundamental formulation of quantum mechanics should exist, which avoids having to use a notion of time. In this paper we discuss as to how such a fundamental formulation could be constructed for single particle, non-relativistic quantum mechanics. We argue that there is an underlying non-linear theory of quantum gravity, to which both standard quantum mechanics and classical general relativity are approximations. The timeless formulation of quantum mechanics follows from the underlying theory when the mass of the particle is much smaller than Planck mass. On the other hand, when the particle's mass is much larger than Planck mass, spacetime emerges and the underlying theory should reduce to classical mechanics and general relativity. We also suggest that noncommutative differential geometry is a possible candidate for describing this underlying theory.
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.
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.
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.
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.
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.
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.
124426353
Lyra's geometry and cosmology: A Review
The Lyra's geometry, which is a generalization of Weyl's geometry (removing the defect of non-integrability of length transfer) and the gravitational theory and cosmology based on this geometry have been reviewed. Further, cosmological models with both constant and time dependent displacement field have been discussed. Some of these models solve the singularity, entropy and horizon problems. Finally some possibilities of further problems and their investigations 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.).
117560530
Confrontation of QMD model with the experimental data for $^{40}Ar$ +$^{45}$Sc, $^{197}Au$ +$^{197}$Au and $^{129}Xe$ +$^{119}$Sn reactions
In the present work, we make confrontation of our theoretical calculations using quantum molecular dynamics model with the experimental data for the reactions of $^{40}Ar$ +$^{45}$Sc, $^{197}Au$ +$^{197}$Au and $^{129}Xe$ +$^{119}$Sn at different incident energies. In these reactions, we display the charge distribution and energy dependence of fragments multiplicity. Our results indicate good agreement with the experimental data for all the reactions.