Approximate Solutions of the Einstein Equations for Isentropic Motions of Plane-Symmetric Distributions of Perfect Fluids

1957 ◽  
Vol 107 (3) ◽  
pp. 884-900 ◽  
Author(s):  
A. H. Taub
Keyword(s):  
Approximate Solutions ◽  
Einstein Equations ◽  
Symmetric Distributions ◽  
Plane Symmetric ◽  
Perfect Fluids

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.

scholarly journals THE CONFORMALLY SPHERICALLY (PLANE-) SYMMETRIC ELECTRO-VACUUM SOLUTION TO EINSTEIN EQUATIONS

1989 ◽  
Vol 38 (7) ◽  
pp. 170
Author(s):  
FAN LI ◽  
LIANG CAN-BIN
Keyword(s):  
Vacuum Solution ◽  
Einstein Equations ◽  
Plane Symmetric

An extension of the plane-symmetric electrovac general solution to Einstein equations

1985 ◽  
Vol 17 (10) ◽  
pp. 1001-1013 ◽  
Author(s):  
Li jian-zeng ◽  
Liang can-bin
Keyword(s):  
General Solution ◽  
Einstein Equations ◽  
Plane Symmetric

General exact solutions of Einstein equations for static perfect fluids with spherical symmetry

1987 ◽  
Vol 28 (12) ◽  
pp. 2949-2950 ◽  
Author(s):  
Sonia Berger ◽  
Roberto Hojman ◽  
Jorge Santamarina
Keyword(s):  
Exact Solutions ◽  
Spherical Symmetry ◽  
Einstein Equations ◽  
Perfect Fluids

scholarly journals Global properties of locally spatially homogeneous cosmological models with matter

1995 ◽  
Vol 118 (3) ◽  
pp. 511-526 ◽  
Author(s):  
Alan D. Rendall
Keyword(s):  
Cosmological Models ◽  
Einstein Equations ◽  
Homogeneous Solutions ◽  
Perfect Fluids ◽  
Global Properties ◽  
Homogeneous Cosmological Models ◽  
Scalar Invariant ◽  
Spatially Homogeneous ◽  
Contracting Phase

AbstractThe existence and nature of singularities in locally spatially homogeneous solutions of the Einstein equations coupled to various phenoraenological matter models is investigated. It is shown that, under certain reasonable assumptions on the matter, there are no singularities in an expanding phase of the evolution and that unless the spacetime is empty a contracting phase always ends in a singularity where at least one scalar invariant of the curvature diverges uniformly. The class of matter models treated includes perfect fluids, mixtures of non-interacting perfect fluids and collisionless matter.

scholarly journals The Glimm scheme for perfect fluids on plane-symmetric Gowdy spacetimes

2004 ◽  
Vol 21 (22) ◽  
pp. 5043-5074 ◽  
Author(s):  
A P Barnes ◽  
P G Lefloch ◽  
B G Schmidt ◽  
J M Stewart
Keyword(s):  
Plane Symmetric ◽  
Glimm Scheme ◽  
Perfect Fluids ◽  
Gowdy Spacetimes

Time-dependent solution from Myers–Perry

2016 ◽  
Vol 94 (2) ◽  
pp. 177-179
Author(s):  
L.A. López ◽  
Omar Pedraza ◽  
V.E. Ceron
Keyword(s):  
Rotational Symmetry ◽  
Space Time ◽  
Einstein Equations ◽  
Time Dependent ◽  
Wick Rotation ◽  
Five Dimensions ◽  
Asymptotically Flat ◽  
Plane Symmetric ◽  
New Interpretation ◽  
Time Dependent Solution

We present a three-parameter time-dependent solution of the vacuum Einstein equations in five dimensions. The solution is obtained by applying the Wick rotation to the Myers–Perry solution that represents a rotating black hole in five dimensions. The new interpretation of the Myers–Perry solution can be considered among the generalized Einstein–Rosen type that can be interpreted as plane-symmetric waves, cylindrical waves or cosmological space–time in five dimensions. In some limits the solution has boost-rotational symmetry and it is asymptotically flat. In the case that the solution represents a cylindrical space–time, the E-energy is analyzed.

scholarly journals A NONSTATIC PLANE-SYMMETRIC SOLUTION OF EINSTEIN EQUATIONS WITH A SPECIAL SCALAR FIELD

1993 ◽  
Vol 42 (2) ◽  
pp. 188
Author(s):  
LI JIAN-ZENG
Keyword(s):  
Scalar Field ◽  
Symmetric Solution ◽  
Einstein Equations ◽  
Plane Symmetric

scholarly journals NAKED SINGULARITIES AS CANDIDATES FOR GAMMA-RAY BURSTERS

1994 ◽  
Vol 03 (03) ◽  
pp. 647-651 ◽  
Author(s):  
SANDIP K. CHAKRABARTI ◽  
PANKAJ S. JOSHI
Keyword(s):  
Gravitational Waves ◽  
Gamma Rays ◽  
Gamma Ray ◽  
Naked Singularity ◽  
Shift Factor ◽  
Red Shift ◽  
Einstein Equations ◽  
Pure Radiation ◽  
Naked Singularities ◽  
Perfect Fluids

Naked singularities appear naturally in dynamically evolving solutions of Einstein equations involving gravitational collapse of radiation, dust, and perfect fluids provided the rate of accretion is less than a critical value. We propose that the gamma-ray bursters (GRBs) are examples of these naked singularity solutions. For illustration, we show that according to solutions involving spherically symmetric collapse of pure radiation field, the energy Eγ and the observed duration Δt0 of a GRB should satisfy, [Formula: see text] being the fraction (10−2 to 10−3) of energy released as gamma rays and the rest possibly as gravitational waves. All the presently observed GRBs satisfy this condition; those satisfying the condition close to equality must necessarily be of cosmological origin with the red-shift factor z not exceeding ~1−10 depending on exact observed flux, red-shift and conversion efficiency of gamma rays. If GRBs are indeed from naked singular regions, they should also be accompanied by a strong burst of gravitational waves which, if detectible, will constitute a basic test for our model.

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