SPHERICAL AND NON-SPHERICAL GRAVITATIONAL COLLAPSE IN MONOPOLE-ANTI-DE SITTER–VAIDYA SPACE–TIME

2006 ◽  
Vol 15 (11) ◽  
pp. 1977-1984 ◽  
Author(s):  
K. D. PATIL ◽  
U. S. THOOL
Keyword(s):  
Gravitational Collapse ◽  
Space Time ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Spherical Collapse ◽  
Time Singularities

In the present work, we investigate the influence of the monopole field on the occurrence of the space–time singularities in the gravitational collapse of anti-de Sitter–Vaidya space–time. It has been found that the spherically symmetric monopole-anti-de Sitter–Vaidya space–time contradicts the CCH, whereas the non-spherical collapse respects it.

scholarly journals HOW TO BYPASS BIRKHOFF THROUGH EXTRA DIMENSIONS: A SIMPLE FRAMEWORK FOR INVESTIGATING THE GRAVITATIONAL COLLAPSE IN VACUUM

2006 ◽  
Vol 15 (12) ◽  
pp. 2217-2222 ◽  
Author(s):  
PIOTR BIZOŃ ◽  
BERND G. SCHMIDT
Keyword(s):  
Gravitational Collapse ◽  
Einstein Equations ◽  
Dimensional System ◽  
Spherically Symmetric ◽  
Asymptotically Flat ◽  
Spherical Collapse ◽  
Geometric Setting ◽  
Birkhoff's Theorem ◽  
Birkhoff’S Theorem ◽  
Odd Dimensions

It is fair to say that our current mathematical understanding of the dynamics of gravitational collapse to a black hole is limited to the spherically symmetric situation and, in fact, even in this case much remains to be learned. The reason is that Einstein's equations become tractable only if they are reduced to a (1 + 1)-dimensional system of partial differential equations. Owing to this technical obstacle, very little is known about the collapse of pure gravitational waves because by Birkhoff's theorem there is no spherical collapse in vacuum. In this essay, we describe a new cohomogeneity-two symmetry reduction of the vacuum Einstein equations in five and higher odd dimensions which evades Birkhoff's theorem and admits time-dependent asymptotically flat solutions. We argue that this model provides an attractive (1 + 1)-dimensional geometric setting for investigating the dynamics of gravitational collapse in vacuum.

INHOMOGENEOUS DUST COLLAPSE WITH COSMOLOGICAL CONSTANT

2005 ◽  
Vol 14 (03n04) ◽  
pp. 707-715 ◽  
Author(s):  
S. G. GHOSH
Keyword(s):  
Cosmological Constant ◽  
Gravitational Collapse ◽  
Dust Cloud ◽  
Cosmic Censorship ◽  
Space Time ◽  
De Sitter ◽  
Naked Singularities ◽  
Asymptotic Flatness ◽  
Sitter Background ◽  
Strong Curvature

We investigate the occurrence of naked singularities in the gravitational collapse of an inhomogeneous dust cloud in an expanding de Sitter background — a piece of Tolman–Bondi–de Sitter space–time. It turns out that the collapse proceed in the same way as in the Minkowski background, i.e., the strong curvature naked singularities form and thus violate the cosmic censorship conjecture. Our result unambiguously support the fact that the asymptotic flatness of space–time is not a necessary ingredient for the development of naked singularities.

scholarly journals Gravitational collapse in anti-de Sitter space–time

2003 ◽  
Vol 571 (3-4) ◽  
pp. 245-249 ◽  
Author(s):  
G.L. Alberghi ◽  
R. Casadio
Keyword(s):  
Gravitational Collapse ◽  
De Sitter Space ◽  
Space Time ◽  
De Sitter

The curvature effect on the gravitational collapse of interacting and non-interacting combination of dark matter and dark energy

2020 ◽  
Vol 35 (17) ◽  
pp. 2050078
Author(s):  
S. Z. Abbas ◽  
H. H. Shah ◽  
W. Chammam ◽  
H. Sun ◽  
Wasim Ul Haq ◽  
...  
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Gravitational Collapse ◽  
Space Time ◽  
Relativistic Astrophysics ◽  
Spherically Symmetric ◽  
Curvature Effect ◽  
De Formula ◽  
General Relativistic

The study of gravitational collapse is a very interesting phenomena in general relativistic astrophysics. Here, in this study we investigated the gravitational collapse of a spherically symmetric core of a star, constituted of dark matter (DM) ([Formula: see text]), in dark energy (DE) ([Formula: see text]) background. It was investigated that gravitational collapse of interacting and noninteracting combination of DM and DE yields BH formation. In this work, our main aim is to examine the effect of space–time curvature [Formula: see text] on the gravitational collapse of interacting and noninteracting combination of dark matter and DE. We achieve the visible influence of curvature on gravitational collapse analytically and interpret the results graphically.

scholarly journals GRAVITATIONAL COLLAPSE OF SPHERICALLY SYMMETRIC PERFECT FLUID WITH KINEMATIC SELF-SIMILARITY

2002 ◽  
Vol 11 (02) ◽  
pp. 155-186 ◽  
Author(s):  
C. F. C. BRANDT ◽  
L.-M. LIN ◽  
J. F. VILLAS DA ROCHA ◽  
A. Z. WANG
Keyword(s):  
Black Holes ◽  
Perfect Fluid ◽  
Gravitational Collapse ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Schwarzschild Solution ◽  
Naked Singularities

Analytic spherically symmetric solutions of the Einstein field equations coupled with a perfect fluid and with self-similarities of the zeroth, first and second kinds, found recently by Benoit and Coley [Class. Quantum Grav.15, 2397 (1998)], are studied, and found that some of them represent gravitational collapse. When the solutions have self-similarity of the first (homothetic) kind, some of the solutions may represent critical collapse but in the sense that now the "critical" solution separates the collapse that forms black holes from the collapse that forms naked singularities. The formation of such black holes always starts with a mass gap, although the "critical" solution has homothetic self-similarity. The solutions with self-similarity of the zeroth and second kinds seem irrelevant to critical collapse. Yet, it is also found that the de Sitter solution is a particular case of the solutions with self-similarity of the zeroth kind, and that the Schwarzschild solution is a particular case of the solutions with self-similarity of the second kind with the index α=3/2.

NATURE OF THE SINGULARITIES IN HIGHER-DIMENSIONAL HUSAIN SPACE–TIME

2006 ◽  
Vol 15 (09) ◽  
pp. 1359-1371 ◽  
Author(s):  
K. D. PATIL ◽  
S. S. ZADE
Keyword(s):  
Gravitational Collapse ◽  
Dimensional Space ◽  
Higher Dimensions ◽  
Cosmic Censorship ◽  
Space Time ◽  
Spherically Symmetric ◽  
Naked Singularities ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
Cosmic Censorship Hypothesis

We generalize the earlier studies on the spherically symmetric gravitational collapse in four-dimensional space–time to higher dimensions. It is found that the central singularities may be naked in higher dimensions but depend sensitively on the choices of the parameters. These naked singularities are found to be gravitationally strong that violate the cosmic censorship hypothesis.

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 SPHERICALLY SYMMETRIC SPACE–TIME WITH REGULAR DE SITTER CENTER

2003 ◽  
Vol 12 (06) ◽  
pp. 1015-1034 ◽  
Author(s):  
IRINA DYMNIKOVA
Keyword(s):  
Black Hole ◽  
Energy Condition ◽  
Space Time ◽  
Cosmological Term ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Sitter Group ◽  
Class Invariant ◽  
Time Symmetry ◽  
De Sitter Vacuum

We formulate the requirements which lead to the existence of a class of globally regular solutions of the minimally coupled GR equations asymptotically de Sitter at the center. The source term for this class, invariant under boosts in the radial direction, is classified as spherically symmetric vacuum with variable density and pressure [Formula: see text] associated with an r-dependent cosmological term [Formula: see text], whose asymptotic at the origin, dictated by the weak energy condition, is the Einstein cosmological term Λgμν, while asymptotic at infinity is de Sitter vacuum with λ < Λ or Minkowski vacuum. For this class of metrics the mass m defined by the standard ADM formula is related to both the de Sitter vacuum trapped at the origin and the breaking of space–time symmetry. In the case of the flat asymptotic, space–time symmetry changes smoothly from the de Sitter group at the center to the Lorentz group at infinity through radial boosts in between. Geometry is asymptotically de Sitter as r → 0 and asymptotically Schwarzschild at large r. In the range of masses m ≥ m crit , the de Sitter–Schwarzschild geometry describes a vacuum nonsingular black hole (ΛBH), and for m < m crit it describes G-lump — a vacuum selfgravitating particle-like structure without horizons. In the case of de Sitter asymptotic at infinity, geometry is asymptotically de Sitter as r → 0 and asymptotically Schwarzschild–de Sitter at large r. Λμν geometry describes, dependently on parameters m and [Formula: see text] and choice of coordinates, a vacuum nonsingular cosmological black hole, self-gravitating particle-like structure at the de Sitter background λgμν, and regular cosmological models with cosmological constant evolving smoothly from Λ to λ.

scholarly journals A Class of Non-Singular Gravi–Dilaton Backgrounds

1997 ◽  
Vol 12 (25) ◽  
pp. 1883-1889 ◽  
Author(s):  
A. Buonanno ◽  
C. Ungarelli ◽  
M. Gasperini
Keyword(s):  
Effective Action ◽  
Finite Size ◽  
Singular Solutions ◽  
Tree Level ◽  
Spherically Symmetric ◽  
De Sitter ◽  
First Order ◽  
Time Singularities ◽  
Symmetric States ◽  
Peak Value

We present a class of static, spherically symmetric, non-singular solutions of the tree-level string effective action, truncated to first order in α′. In the string frame the solutions approach asymptotically (as r→ 0 and r→∞) two different anti-de Sitter configurations, thus interpolating between two maximally symmetric states of different constant curvatures. The radial-dependent dilaton defines a string coupling which is everywhere finite, with a peak value that can be chosen arbitrarily small so as to neglect quantum-loop corrections. This example stresses the possible importance of finite-size α′ corrections, typical of string theory, in avoiding space–time singularities.

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