gr-qc/0609094 Gravitationally Collapsing Shells in (2+1) Dimensions (original) (raw)
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gr-qc/0609093 Gravitationally Collapsing Shells in (2+1) Dimensions
2006
We study gravitationally collapsing models of pressureless dust, fluids with pressure, and the generalized Chaplygin gas (GCG) shell in (2+1)-dimensional spacetimes. Various collapse scenarios are investigated under a variety of the background configurations such as anti-de Sitter(AdS) black hole, de Sitter (dS) space, flat and AdS space with a conical deficit. As with the case of a disk of dust, we find that the collapse of a dust shell coincides with the Oppenheimer-Snyder type collapse to a black hole provided the initial density is sufficiently large. We also find – for all types of shell – that collapse to a naked singularity is possible under a broad variety of initial conditions. For shells with pressure this singularity can occur for a finite radius of the shell. We also find that GCG shells exhibit diverse collapse scenarios, which can be easily demonstrated by an effective potential analysis.
Erratum: Gravitationally collapsing shells in (2+1) dimensions [Phys. Rev. D 74, 124016 (2006)]
Physical Review D, 2008
We study gravitationally collapsing models of pressureless dust, fluids with pressure, and the generalized Chaplygin gas (GCG) shell in (2+1)-dimensional spacetimes. Various collapse scenarios are investigated under a variety of the background configurations such as anti-de Sitter(AdS) black hole, de Sitter (dS) space, flat and AdS space with a conical deficit. As with the case of a disk of dust, we find that the collapse of a dust shell coincides with the Oppenheimer-Snyder type collapse to a black hole provided the initial density is sufficiently large. We also find-for all types of shell-that collapse to a naked singularity is possible under a broad variety of initial conditions. For shells with pressure this singularity can occur for a finite radius of the shell. We also find that GCG shells exhibit diverse collapse scenarios, which can be easily demonstrated by an effective potential analysis.
Relativistic Gravitational Collapse of a Cylindrical Shell of Dust
Progress of Theoretical Physics, 2007
The gravitational collapse of a thick cylindrical shell of dust matter is investigated. It is found that a spacetime singularity forms on the symmetry axis and that it is necessarily naked, i.e., observable in principle. We propose a physically reasonable boundary condition at this naked singularity to construct the solution including its causal future. This boundary condition enables us to construct the unique continuation of spacetime beyond the naked singularity and ensures that the dust shell passes through the naked singularity. When the cylindrical shell leaves its symmetry axis away, the naked singularity disappears, and regularity is recovered. We construct numerical solutions with this feature. This result implies that the gravity produced by a thick cylindrical shell of dust is too weak to bind the shell even if it engenders the formation of a curvature singularity which is so strong as to satisfy the limiting focusing condition. For this reason, this naked singularity is very weak in the extended spacetime; the metric tensor is C 1− even at the naked singularity, and the extended spacetime is complete for almost all geodesics. This feature is also seen for singular hypersurfaces. Such an extended spacetime can be regarded as phenomenological in the sense that it is valid if the relevant microphysics length scale is sufficiently small compared to the scale of interest.
Progress of Theoretical Physics, 2009
The gravitational collapse of a thick cylindrical shell of dust matter is investigated. It is found that a spacetime singularity forms on the symmetry axis and that it is necessarily naked, i.e., observable in principle. We propose a physically reasonable boundary condition at this naked singularity to construct the solution including its causal future. This boundary condition enables us to construct the unique continuation of spacetime beyond the naked singularity and ensures that the dust shell passes through the naked singularity. When the cylindrical shell leaves its symmetry axis away, the naked singularity disappears, and regularity is recovered. We construct numerical solutions with this feature. This result implies that the gravity produced by a thick cylindrical shell of dust is too weak to bind the shell even if it engenders the formation of a curvature singularity which is so strong as to satisfy the limiting focusing condition. For this reason, this naked singularity is very weak in the extended spacetime; the metric tensor is C 1− even at the naked singularity, and the extended spacetime is complete for almost all geodesics. This feature is also seen for singular hypersurfaces. Such an extended spacetime can be regarded as phenomenological in the sense that it is valid if the relevant microphysics length scale is sufficiently small compared to the scale of interest.
Shell-crossings in gravitational collapse
An important issue in the study of continual gravitational collapse of a massive matter cloud in general relativity is whether shell-crossing singularities develop as the collapse evolves. We examine this here to show that for any spherically symmetric collapse in general, till arbitrarily close to the final singularity, there is always a finite neighborhood of the center in which there are no shell-crossings taking place. It follows that in order to study the visibility or otherwise of the ultra-dense region close to the final singularity of collapse where physical radius of the matter cloud shrinks to an arbitrarily small value, we can always consider without loss of generality a collapsing ball of finite comoving radius in which there are no shell-crossings.
A Model of Dustlike Spherically Symmetric Gravitational Collapse without Event Horizon Formation
2014
Some dynamical aspects of gravitational collapse are explored in this paper. A timedependent spherically symmetric metric is proposed and the corresponding Einstein field equations are derived. An ultrarelativistic dust-like stress-momentum tensor is considered to obtain analytical solutions of these equations, with the perfect fluid consisting of two purely radial fluxes-the inwards flux of collapsing matter and the outwards flux of thermally emitted radiation. Thermal emission is calculated by means of a simplistic but illustrative model of uninteracting collapsing shells. Our results show an asymptotic approach to a maximal space-time deformation without the formation of event horizons. The size of the body is slightly larger than the Schwarzschild radius during most of its lifetime, so that there is no contradiction with either observations or previous theorems on black holes. The relation of the latter with our results is scrutinized in detail.
Gravitational Collapse of a Shell of Quantized Matter
1998
The semi-classical collapse, including lowest order back-reaction, of a thin shell of self-gravitating quantized matter is illustrated. The conditions for which selfgravitating matter forms a thin shell are first discussed and an effective Lagrangian for such matter is obtained. The matter-gravity system is then quantized, the semiclassical limit for gravitation is taken and the method of adiabatic invariants is applied to the resulting time dependent matter Hamiltonian. The governing equations are integrated numerically, for suitable initial conditions, in order to illustrate the effect of back-reaction, due to the creation of matter, in slowing down the collapse near the horizon. *
Gravitational Collapse of a Charged Shell
2012
The junction formalism is applied to study the gravitational collapse of charged spherical shell. The modeling is based on the radiation fluid singular hypersurface filled with physical vacuum. The barotropic fluids with the linear equation of state are considered. An equation governing the behavior of the physical vacuum energy density is deduced. Our result show that, no charge can stop the gravitational collapse of the shell below the upper Reissner-Nordstrom radius.
Gravitational collapse and formation of a black hole in a type II minimally modified gravity theory
Journal of Cosmology and Astroparticle Physics
We study the spherically symmetric collapse of a cloud of dust in VCDM, a class of gravitational theories with two local physical degrees of freedom. We find that the collapse corresponds to a particular foliation of the Oppenheimer-Snyder solution in general relativity (GR) which is endowed with a constant trace for the extrinsic curvature relative to the time t constant foliation. For this solution, we find that the final state of the collapse leads to a static configuration with the lapse function vanishing at a radius inside the apparent horizon. Such a point is reached in an infinite time-t interval, t being the cosmological time, i.e. the time of an observer located far away from the collapsing cloud. The presence of this vanishing lapse endpoint implies the necessity of a UV completion to describe the physics inside the resulting black hole. On the other hand, since the corresponding cosmic time t is infinite, VCDM can safely describe the whole history of the universe at larg...
Role of angular momentum and cosmic censorship in (2+1)-dimensional rotating shell collapse
Physical Review D, 2009
We study the gravitational collapse problem of rotating shells in three-dimensional Einstein gravity with and without a cosmological constant. Taking the exterior and interior metrics to be those of stationary metrics with asymptotically constant curvature, we solve the equations of motion for the shells from the Darmois-Israel junction conditions in the co-rotating frame. We study various collapse scenarios with arbitrary angular momentum for a variety of geometric configurations, including anti-de Sitter, de Sitter, and flat spaces. We find that the collapsing shells can form a BTZ black hole, a three-dimensional Kerr-dS spacetime, and an horizonless geometry of point masses under certain initial conditions. For pressureless dust shells, the curvature singularity is not formed due to the angular momentum barrier near the origin. However when the shell pressure is nonvanishing, we find that for all types of shells with polytropic-type equations of state (including the perfect fluid and the generalized Chaplygin gas), collapse to a naked singularity is possible under generic initial conditions. Angular momentum does not in general guard against violation of cosmic censorship.