The eternal naked singularity formation in the case of gravitational collapse of generalized Vaidya space–time

2018 ◽  
Vol 33 (17) ◽  
pp. 1850102 ◽  
Author(s):  
Vitalii Vertogradov
Keyword(s):  
Gravitational Collapse ◽  
Negative Pressure ◽  
Apparent Horizon ◽  
Naked Singularity ◽  
Space Time ◽  
Matter Field ◽  
Type I ◽  
The Past ◽  
Central Singularity ◽  
Short Time

In this paper, we consider the gravitational collapse of generalized Vaidya space–time when the matter satisfies the equation of the state either [Formula: see text] or [Formula: see text], where [Formula: see text]. We show that in the case when type I of matter field is dust, then the apparent horizon will never appear but there is no a family of null radial future-directed geodesics which terminate at the central singularity in the past. Also, we show that in the case of negative pressure, the result of the gravitational collapse might be the naked singularity and the apparent horizon appears and in very short time disappears again. In the case of the negative pressure, we show that the result of the gravitational collapse might be the eternal naked singularity.

scholarly journals GENERICITY ASPECTS IN GRAVITATIONAL COLLAPSE TO BLACK HOLES AND NAKED SINGULARITIES

2012 ◽  
Vol 21 (08) ◽  
pp. 1250066 ◽  
Author(s):  
PANKAJ S. JOSHI ◽  
DANIELE MALAFARINA ◽  
RAVINDRA V. SARAYKAR
Keyword(s):  
Black Holes ◽  
Initial Data ◽  
Gravitational Collapse ◽  
Naked Singularity ◽  
Matter Field ◽  
Einstein Equations ◽  
Type I ◽  
Naked Singularities ◽  
Physical Conditions ◽  
Perfect Fluids

Here we investigate the genericity and stability aspects for naked singularities and black holes that arise as the final states for a complete gravitational collapse of a spherical massive matter cloud. The form of the matter considered is a general Type I matter field, which includes most of the physically reasonable matter fields such as dust, perfect fluids and such other physically interesting forms of matter widely used in gravitation theory. Here, we first study in some detail the effects of small pressure perturbations in an otherwise pressure-free collapse scenario, and examine how a collapse evolution that was going to the black hole endstate would be modified and go to a naked singularity, once small pressures are introduced in the initial data. This allows us to understand the distribution of black holes and naked singularities in the initial data space. Collapse is examined in terms of the evolutions allowed by Einstein equations, under suitable physical conditions and as evolving from a regular initial data. We then show that both black holes and naked singularities are generic outcomes of a complete collapse, when genericity is defined in a suitable sense in an appropriate space.

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 The Negative Energy in Generalized Vaidya Spacetime

Universe ◽  
2020 ◽  
Vol 6 (9) ◽  
pp. 155
Author(s):  
Vitalii Vertogradov
Keyword(s):  
Gravitational Collapse ◽  
Naked Singularity ◽  
Negative Energy ◽  
Matter Field ◽  
The State ◽  
Energy Problem

In this paper we consider the negative energy problem in generalized Vaidya spacetime. We consider several models where we have the naked singularity as a result of the gravitational collapse. In these models we investigate the geodesics for particles with negative energy when the II type of the matter field satisfies the equation of the state P=αρ (α∈[0,1]).

scholarly journals Stability of naked singularity arising in gravitational collapse of Type I matter fields

Pramana ◽  
2005 ◽  
Vol 65 (1) ◽  
pp. 17-33 ◽  
Author(s):  
Sanjay B. Sarwe ◽  
R. V. Saraykar
Keyword(s):  
Gravitational Collapse ◽  
Naked Singularity ◽  
Type I ◽  
Matter Fields

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 NON-MARGINALLY BOUND INHOMOGENEOUS DUST COLLAPSE IN HIGHER DIMENSIONAL SPACE–TIME

2003 ◽  
Vol 12 (04) ◽  
pp. 639-648 ◽  
Author(s):  
S. G. GHOSH ◽  
A. BANERJEE
Keyword(s):  
Gravitational Collapse ◽  
Dimensional Space ◽  
Dust Cloud ◽  
Naked Singularity ◽  
Space Time ◽  
Higher Dimensional Space Time ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
Self Similar

We investigate the occurrence and nature of a naked singularity in the gravitational collapse of an inhomogeneous dust cloud described by a self-similar higher dimensional Tolman–Bondi space–time. Bound, marginally bound and unbound space–times are analyzed. The degree of inhomogeneity of the collapsing matter necessary to form a naked singularity is given.

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.

World Economy: Prospects and Barriers for Recovery

2012 ◽  
pp. 61-83 ◽  
Author(s):  
M. Ershov
Keyword(s):  
World Economy ◽  
Western World ◽  
Short Time Period ◽  
Market Segments ◽  
Junk Bonds ◽  
The Past ◽  
Time Period ◽  
The Us ◽  
Global Liquidity ◽  
Short Time

According to the latest forecasts, it will take 10 years for the world economy to get back to “decent shape”. Some more critical estimates suggest that the whole western world will have a “colossal mess” within the next 5–10 years. Regulators of some major countries significantly and over a short time‑period changed their forecasts for the worse which means that uncertainty in the outlook for the future persists. Indeed, the intensive anti‑crisis measures have reduced the severity of the past problems, however the problems themselves have not disappeared. Moreover, some of them have become more intense — the eurocrisis, excessive debts, global liquidity glut against the backdrop of its deficit in some of market segments. As was the case prior to the crisis, derivatives and high‑risk operations with “junk” bonds grow; budget problems — “fiscal cliff” in the US — and other problems worsen. All of the above forces the regulators to take unprecedented (in their scope and nature) steps. Will they be able to tackle the problems which emerge?

The Kalam Cosmological Argument

2018 ◽  
Author(s):  
William Lane Craig
Keyword(s):  
Space Time ◽  
Cosmological Argument ◽  
Philosophical Literature ◽  
The Past ◽  
Classical Space ◽  
Kalam Cosmological Argument ◽  
Kalām Cosmological Argument ◽  
The Universe

A survey of recent philosophical literature on the kalam cosmological argument reveals that arguments for the finitude of the past and, hence, the beginning of the universe remain robust. Plantinga’s brief criticisms of Kant’s argument in his First Antinomy concerning time are shown not to be problematic for the kalam argument. This chapter addresses, one by one, the two premises of the kalam, focusing on their philosophical aspects. The notion of infinity, both actual and potential, is discussed in relation to the coming into being of the universe. In addition, the scientific aspects of the two premises are also, briefly, addressed. Among these are the Borde-Guth-Vilenkin theorem, which proves that classical space-time cannot be extended to past infinity but must reach a boundary at some time in the finite past. This, among other factors, lends credence to the kalam argument’s second premise.

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