scholarly journals Singularities and self-similarity in gravitational collapse

2019 ◽  
Author(s):  
Tomohiro Harada
Keyword(s):  
Gravitational Collapse ◽  
Self Similarity

scholarly journals COLLAPSING SCALAR FIELD WITH KINEMATIC SELF-SIMILARITY OF THE SECOND KIND IN (2+1) GRAVITY

2005 ◽  
Vol 14 (06) ◽  
pp. 1049-1061 ◽  
Author(s):  
R. CHAN ◽  
M. F. A. DA SILVA ◽  
J. F. VILLAS DA ROCHA ◽  
ANZHONG WANG
Keyword(s):  
Black Holes ◽  
Scalar Field ◽  
Gravitational Collapse ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Field Equations ◽  
Self Similarity ◽  
Global Properties ◽  
Scalar Field Equations

All the (2+1)-dimensional circularly symmetric solutions with kinematic self-similarity of the second kind to the Einstein-massless-scalar field equations are found and their local and global properties are studied. It is found that some of them represent gravitational collapse of a massless scalar field, in which black holes are always formed.

scholarly journals EPISODIC SELF-SIMILARITY IN CRITICAL GRAVITATIONAL COLLAPSE

2002 ◽  
pp. 1670-1671
Author(s):  
J. THORNBURG ◽  
CH. LECHNER ◽  
M. PÜRRER ◽  
P. C. AICHELBURG ◽  
S. HUSA
Keyword(s):  
Gravitational Collapse ◽  
Self Similarity

scholarly journals Critical phenomena in gravitational collapse of Husain–Martinez–Nunez scalar field

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Xiaobao Wang ◽  
Xiaoning Wu ◽  
Sijie Gao
Keyword(s):  
Scalar Field ◽  
Critical Phenomena ◽  
Gravitational Collapse ◽  
Naked Singularity ◽  
Extrinsic Curvature ◽  
Analytical Models ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Self Similarity ◽  
Metric Function

Abstract We construct analytical models to study the critical phenomena in gravitational collapse of the Husain-Martinez-Nunez massless scalar field. We first use the cut-and-paste technique to match the conformally flat solution ($$c=0$$c=0 ) onto an outgoing Vaidya solution. To guarantee the continuity of the metric and the extrinsic curvature, we prove that the two solutions must be joined at a null hypersurface and the metric function in Vaidya spacetime must satisfy certain constraints. We find that the mass of the black hole in the resulting spacetime takes the form $$M\propto (p-p^*)^\gamma $$M∝(p-p∗)γ, where the critical exponent $$\gamma $$γ is equal to 0.5. For the case $$c\ne 0$$c≠0, we show that the scalar field must be joined onto two pieces of Vaidya spacetimes to avoid a naked singularity. We also derive the power-law mass formula with $$\gamma =0.5$$γ=0.5. Compared with previous analytical models which were constructed from a different scalar field with continuous self-similarity, we obtain the same value of $$\gamma $$γ. However, we show that the solution with $$c\ne 0$$c≠0 is not self-similar. Therefore, we provide a rare example that a scalar field without self-similarity also possesses the features of critical collapse.

scholarly journals GRAVITATIONAL COLLAPSE OF A MASSLESS SCALAR FIELD AND A PERFECT FLUID WITH SELF-SIMILARITY OF THE FIRST KIND IN 2+1 DIMENSIONS

2008 ◽  
Vol 17 (11) ◽  
pp. 2143-2158 ◽  
Author(s):  
F. I. M. PEREIRA ◽  
R. CHAN
Keyword(s):  
Black Holes ◽  
Scalar Field ◽  
Perfect Fluid ◽  
Gravitational Collapse ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Self Similarity ◽  
Global Properties ◽  
Self Similar ◽  
Similar Solutions

Self-similar solutions of a collapsing perfect fluid and a massless scalar field with kinematic self-similarity of the first kind in 2+1 dimensions are obtained. The local and global properties of the solutions are studied. It is found that some of them represent gravitational collapse, in which black holes are always formed, and some may be interpreted as representing cosmological models.

GRAVITATIONAL COLLAPSE AND NON-SELF-SIMILARITY IN THE L–T RELATION

2005 ◽  
Vol 14 (05) ◽  
pp. 849-859
Author(s):  
ANTONINO DEL POPOLO ◽  
N. ERCAN ◽  
N. HIOTELIS
Keyword(s):  
Angular Momentum ◽  
Gravitational Collapse ◽  
External Pressure ◽  
Fundamental Result ◽  
Clusters Of Galaxies ◽  
X Rays ◽  
Self Similarity ◽  
Temperature Relation ◽  
Pressure Term ◽  
Self Similar

We derive the luminosity–temperature relation for clusters of galaxies by means of a modification of the self-similar model to take account of angular momentum acquisition by protostructures and of an external pressure term in the virial theorem. We show that the above effect leads, in X-rays, to a luminosity–temperature relation that scales as L ∝ T5, at scale of groups, flattening to L ∝ T3 for rich clusters and converging to L ∝ T2 at higher temperatures. The fundamental result of the model is that gravitational collapse, which takes account of angular momentum acquisition, can explain the non-self-similarity in the L–T relation, in disagreement with the largely accepted assumption that heating/cooling processes and similar are fundamental in the originating the non-self-similar behavior (shaping) of the L–T relation.

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.

GRAVITATIONAL COLLAPSE OF SPHERICALLY SYMMETRIC ANISOTROPIC FLUID WITH HOMOTHETIC SELF-SIMILARITY

2003 ◽  
Vol 12 (07) ◽  
pp. 1315-1332 ◽  
Author(s):  
C. F. C. BRANDT ◽  
M. F. A. DA SILVA ◽  
JAIME F. VILLAS DA ROCHA ◽  
R. CHAN
Keyword(s):  
Physical Properties ◽  
Gravitational Collapse ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Tangential Pressure

We study spacetimes of spherically symmetric anisotropic fluid with homothetic self-similarity. We find a class of solutions to the Einstein field equations by assuming that the tangential pressure of the fluid is proportional to its radial one and that the fluid moves along time-like geodesics. The energy conditions, and geometrical and physical properties of these solutions are studied and found that some of them represent gravitational collapse of an anisotropic fluid.

GRAVITATIONAL COLLAPSE OF A MASSLESS SCALAR FIELD AND A PERFECT FLUID WITH SELF-SIMILARITY OF THE SECOND KIND IN (2 + 1) DIMENSIONS

2006 ◽  
Vol 15 (02) ◽  
pp. 131-152 ◽  
Author(s):  
F. I. M. PEREIRA ◽  
R. CHAN ◽  
AN ZHONG WANG
Keyword(s):  
Black Holes ◽  
Scalar Field ◽  
Perfect Fluid ◽  
Gravitational Collapse ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Self Similarity ◽  
Global Properties ◽  
Self Similar ◽  
Similar Solutions

Self-similar solutions of a collapsing perfect fluid and a massless scalar field with kinematic self-similarity of the second kind in (2 + 1) dimensions are obtained. The local and global properties of the solutions are studied. It is found that some of them represent gravitational collapse, in which black holes are always formed, and some may be interpreted as representing cosmological models.

Sign in / Sign up

Export Citation Format

Share Document