scholarly journals CAN GRAVITATIONAL COLLAPSE SUSTAIN SINGULARITY-FREE TRAPPED SURFACES?

2008 ◽  
Vol 17 (01) ◽  
pp. 165-177 ◽  
Author(s):  
MANASSE R. MBONYE ◽  
DEMOS KAZANAS
Keyword(s):  
Black Hole ◽  
Gravitational Collapse ◽  
Null Geodesic ◽  
Space Time ◽  
Test Case ◽  
Hole Center ◽  
Singularity Formation ◽  
Trapped Surfaces ◽  
Type D ◽  
Fluid Formation

In singularity-generating space–times both the outgoing and the ingoing expansions of null geodesic congruences θ+ and θ- should become increasingly negative without bound, inside the horizon. This behavior leads to geodetic incompleteness, which in turn predicts the existence of a singularity. In this work we inquire whether, in gravitational collapse, space–time can sustain singularity-free trapped surfaces, in the sense that such a space–time remains geodetically complete. As a test case, we consider a type D space–time of Dymnikova which is Schwarzschild-like at large distances and consists of a fluid with a p = -ρ equation of state near r = 0. By following both the expansion parameters θ+ and θ- across the horizon and into the black hole, we find that both θ+ and θ+θ- have turning points inside the trapped region. Further, we find that deep inside the black hole there is a region, 0 ≤ r < r0 (which includes the black hole center), which is not trapped. Thus the trapped region is bounded from both outside and inside. The space–time is geodetically complete, a result which violates a condition for singularity formation. It is inferred that, in general, if gravitational collapse were to proceed with a p =-ρ fluid formation, the resulting black hole might be singularity-free.

scholarly journals Gravitational Collapse

1974 ◽  
Vol 64 ◽  
pp. 82-91 ◽  
Author(s):  
R. Penrose
Keyword(s):  
Black Hole ◽  
Gravitational Collapse ◽  
Naked Singularity ◽  
Cosmic Censorship ◽  
Space Time ◽  
Local Version ◽  
Time Singularities ◽  
Standard Picture ◽  
Cosmic Censorship Hypothesis ◽  
Definition Of

In the standard picture of gravitational collapse to a black hole, a key role is played by the hypothesis of cosmic censorship – according to which no naked space-time singularities can result from any collapse. A precise definition of a naked singularity is given here which leads to a strong ‘local’ version of the cosmic censorship hypothesis. This is equivalent to the proposition that a Cauchy hypersurface exits for the space-time. The principle that the surface area of a black hole can never decrease with time is presented in a new and simplified form which generalizes the earlier statements. A discussion of the relevance of recent work to the naked singularity problem is also given.

scholarly journals Efficient gravitational lens optical scalars calculation of black holes with angular momentum

2019 ◽  
Vol 492 (3) ◽  
pp. 3763-3778
Author(s):  
Ezequiel F Boero ◽  
Osvaldo M Moreschi
Keyword(s):  
Black Hole ◽  
Null Geodesic ◽  
Space Time ◽  
Gravitational Lens ◽  
Hidden Symmetries ◽  
Kerr Geometry ◽  
Deviation Equation ◽  
Efficient Calculation ◽  
Efficient Integration ◽  
Kerr Space

ABSTRACT We provide new very simple and compact expressions for the efficient calculation of gravitational lens optical scalars for Kerr space–time, which are exact along any null geodesic. These new results are obtained recurring to well-known results on geodesic motion that exploit obvious and hidden symmetries of Kerr space–time and contrast with the rather long and cumbersome expressions previously reported in the literature, providing a helpful improvement for the sake of an efficient integration of the geodesic deviation equation on Kerr geometry. We also introduce a prescription for the observer frame that captures a new notion of centre of the black hole, which can be used for any position of the observer, including those near the black hole. We compare the efficient calculation of weak lens optical scalars with the exact equations, finding an excellent agreement.

scholarly journals GRAVITATIONAL COLLAPSE WITH TANGENTIAL PRESSURE

2011 ◽  
Vol 20 (04) ◽  
pp. 463-495 ◽  
Author(s):  
DANIELE MALAFARINA ◽  
PANKAJ S. JOSHI
Keyword(s):  
Black Hole ◽  
Gravitational Collapse ◽  
Dust Cloud ◽  
Naked Singularity ◽  
Final States ◽  
Singularity Formation ◽  
Tangential Pressure ◽  
Final State ◽  
Collapse Models

Using the general formalism for spherical gravitational collapse developed in [P. S. Joshi and I. H. Dwivedi, Class. Quant. Grav.16 (1999) 41; P. S. Joshi and R. Goswami, Phys. Rev. D76 (2007) 084026], we investigate here the final fate of a spherical distribution of a matter cloud, where radial pressures vanish but tangential pressures are nonzero. Within this framework, firstly we examine the effect of introducing a generic small pressure in a well-known black hole formation process, which is that of an otherwise pressure-free dust cloud. The intriguing result we find is that a dust collapse that was going to a black hole final state could now go to a naked singularity final configuration, when arbitrarily small tangential pressures are introduced. The implications of such a scenario are discussed in some detail. Secondly, the approach here allows us to generalize the earlier results obtained on gravitational collapse with nonzero tangential pressure, in the presence of a nonzero cosmological constant. Finally, we discuss the genericity of black hole and naked singularity formation in collapse with nonzero tangential pressure. The treatment here gives a unified and complete picture on collapse final states, in terms of black hole and naked singularity formation, generalizing the earlier results obtained for this class of collapse models. Thus the role of tangential stresses towards determining collapse end-states emerges in a straightforward and transparent manner in our treatment.

scholarly journals The singularities of gravitational collapse and cosmology

1970 ◽  
Vol 314 (1519) ◽  
pp. 529-548 ◽  
Keyword(s):  
Gravitational Collapse ◽  
Null Geodesic ◽  
Energy Condition ◽  
Realistic Model ◽  
Space Time ◽  
Null Cone ◽  
The Past ◽  
Time Singularities ◽  
Trapped Surface ◽  
The Universe

A new theorem on space-time singularities is presented which largely incorporates and generalizes the previously known results. The theorem implies that space-time singularities are to be expected if either the universe is spatially closed or there is an ‘object’ undergoing relativistic gravitational collapse (existence of a trapped surface) or there is a point p whose past null cone encounters sufficient matter that the divergence of the null rays through p changes sign somewhere to the past of p (i. e. there is a minimum apparent solid angle, as viewed from p for small objects of given size). The theorem applies if the following four physical assumptions are made: (i) Einstein’s equations hold (with zero or negative cosmological constant), (ii) the energy density is nowhere less than minus each principal pressure nor less than minus the sum of the three principal pressures (the ‘energy condition’), (iii) there are no closed timelike curves, (iv) every timelike or null geodesic enters a region where the curvature is not specially alined with the geodesic. (This last condition would hold in any sufficiently general physically realistic model.) In common with earlier results, timelike or null geodesic incompleteness is used here as the indication of the presence of space-time singularities. No assumption concerning existence of a global Cauchy hypersurface is required for the present theorem.

scholarly journals Gravitational collapse in Vaidya space–time for Galileon gravity theory

2014 ◽  
Vol 92 (11) ◽  
pp. 1474-1480 ◽  
Author(s):  
Prabir Rudra ◽  
Ujjal Debnath
Keyword(s):  
Gravitational Collapse ◽  
Null Geodesic ◽  
Space Time ◽  
Gravity Theory ◽  
Effective Theory ◽  
Eos Parameter ◽  
Brane Model ◽  
Collapse State ◽  
Wide Range ◽  
Basic Objective

The motive of this work is to study gravitational collapse in Vaidya space–time embedded in Galileon gravity theory. Galileon gravity is in fact an infrared modification of Einstein gravity, which was proposed as a generalization of the four-dimensional effective theory in the DGP brane model. Vaidya’s metric is used all over to follow the nature of future outgoing radial null geodesics. Detecting whether the central singularity is naked or wrapped by an event horizon, by the existence of future directed radial null geodesic emitted in the past from the singularity is the basic objective. To point out the existence of a positive trajectory tangent solution, both particular parametric cases (through tabular forms) and wide range contouring process have been applied. Precisely, the equation of state (EoS) in a perfect fluid satisfies a wide range of phenomena: from dust to exotic fluids like dark energy. We have used the EoS parameter, k, to determine the end collapse state in different cosmological eras.

Geodesic structure of the Clifton–Barrow black hole space–time

2019 ◽  
Vol 34 (22) ◽  
pp. 1950123
Author(s):  
Li-Li Shi ◽  
Jian-Ping Hu ◽  
Yu Zhang ◽  
Chen Ma ◽  
Peng-Fei Duan
Keyword(s):  
Black Hole ◽  
Circular Orbit ◽  
Orbital Motion ◽  
Null Geodesic ◽  
Space Time ◽  
Circular Orbits ◽  
Test Particles ◽  
Stable Circular Orbit ◽  
Geodesic Structure ◽  
Bound Orbits

In this paper, we investigate the geodesic structure of Clifton–Barrow black hole space–time. Through the numerical analysis of the effective potential and the motion equation, the orbital types of test particles and photons and the corresponding orbital motion diagrams of each orbital types under certain conditions are obtained. We find that angular momentum [Formula: see text] and [Formula: see text] determine the existence of bound orbits and circular orbits. And we also find that the radius of unstable circular orbit decreases with increases in [Formula: see text] while the radius of stable circular orbit increases. Furthermore, as [Formula: see text] increases, the radius of unstable circular orbit increases, while the radius of stable circular orbit decreases. For null geodesic, parameters [Formula: see text] and [Formula: see text] do not affect the types of null orbits. The radius of the unstable circular orbits increases with the increase of [Formula: see text]. However, the radius of the unstable circular orbits remains unchanged as [Formula: see text] increases. Also, we show that the precession direction of the bound orbits of the test particles is counterclockwise for [Formula: see text], but clockwise with [Formula: see text]. Moreover, different energy values have an effect on the curvature of escape and absorb orbits curve.

NEGATIVE ENERGY DENSITY IN SPINNING MATTER SOURCES IN WORMHOLE SPACE–TIMES WITH TORSION

1998 ◽  
Vol 13 (38) ◽  
pp. 3069-3072
Author(s):  
L. C. GARCIA DE ANDRADE
Keyword(s):  
Energy Density ◽  
Spin Density ◽  
Gravitational Collapse ◽  
Negative Pressure ◽  
Negative Energy ◽  
Space Time ◽  
Negative Energy Density ◽  
Traversable Wormholes ◽  
Radial Tension

Negative energy densities in spinning matter sources of non-Riemannian ultrastatic traversable wormholes require the spin energy density to be higher than the negative pressure or the radial tension. Since the radial tension necessary to support wormholes is higher than the spin density in practice, it seems very unlikely that wormholes supported by torsion may exist in nature. This result corroborates earlier results by Soleng against the construction of the closed time-like curves (CTC) in space–time geometries with spin and torsion. It also agrees with earlier results by Kerlick according to which Einstein–Cartan (EC) gravity torsion sometimes enhance the gravitational collapse instead of avoiding it.

scholarly journals DIRECTLY OBSERVING ENTROPY ACCUMULATION ON THE HORIZON AND HOLOGRAPHY

2012 ◽  
Vol 21 (11) ◽  
pp. 1242010
Author(s):  
ARIEL EDERY ◽  
HUGUES BEAUCHESNE
Keyword(s):  
Black Hole ◽  
Numerical Simulations ◽  
Gravitational Collapse ◽  
Spherical Symmetry ◽  
Proper Time ◽  
Horizon Area

Recent numerical simulations of gravitational collapse show that there exists a special foliation of the spacetime where matter and entropy accumulate directly on the inside of the horizon surface. In this foliation, the time coincides with the proper time of the asymptotic static observer (ASO) and for spherical symmetry, this corresponds to isotropic co-ordinates. In this gauge, the three-volume in the interior shrinks to zero and only the horizon area remains at the end of collapse. In a different foliation, matter and entropy accumulate in the volume. The entropy is however independent of the foliation. Black hole holography is therefore a mapping from an arbitrary foliation, where information resides in the volume, to the special ASO frame, where it resides directly on the horizon surface.

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