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 POSSIBLE WAY OUT OF THE HAWKING PARADOX: ERASING THE INFORMATION AT THE HORIZON

2008 ◽  
Vol 17 (13n14) ◽  
pp. 2507-2514 ◽  
Author(s):  
L. HERRERA
Keyword(s):  
Gravitational Field ◽  
Exact Solutions ◽  
Spherical Symmetry ◽  
Apparent Horizon ◽  
Information Loss ◽  
Einstein Equations ◽  
Small Deviations ◽  
Information Loss Paradox ◽  
Landauer’S Principle

We show that small deviations from spherical symmetry, described by means of exact solutions to Einstein equations, provide a mechanism to "bleach" the information about the collapsing body as it falls through the apparent horizon, thereby resolving the information loss paradox. The resulting picture and its implication related to Landauer's principle in the presence of a gravitational field is discussed.

scholarly journals Using Algebraic Computing To Teach General Relativity And Cosmology

2012 ◽  
Vol 56 (1) ◽  
pp. 139-144
Author(s):  
Dumitru N. Vulcanov ◽  
Remus-Ştefan Ş. Boată
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Undergraduate Students ◽  
Computer Algebra ◽  
Computer Algebra System ◽  
Einstein Equations ◽  
Algebraic Programming ◽  
Algebraic Computing

AbstractThe article presents some new aspects and experience on the use of computer in teaching general relativity and cosmology for undergraduate students (and not only) with some experience in computer manipulation. Some years ago certain results were reported [1] using old fashioned computer algebra platforms but the growing popularity of graphical platforms as Maple and Mathematica forced us to adapt and reconsider our methods and programs. We will describe some simple algebraic programming procedures (in Maple with GrTensorII package) for obtaining and the study of some exact solutions of the Einstein equations in order to convince a dedicated student in general relativity about the utility of a computer algebra system.

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 A Modified Thermodynamics Method to Generate Exact Solutions of Einstein Equations

2017 ◽  
Vol 67 (1) ◽  
pp. 41 ◽  
Author(s):  
Hong-Wei Tan ◽  
Jin-Bo Yang ◽  
Tang-Mei He ◽  
Jing-Yi Zhang
Keyword(s):  
Exact Solutions ◽  
Einstein Equations

scholarly journals ON GENERAL SOLUTIONS OF EINSTEIN EQUATIONS

2011 ◽  
Vol 08 (01) ◽  
pp. 9-21 ◽  
Author(s):  
S. VACARU
Keyword(s):  
Partial Differential Equations ◽  
Cosmological Constant ◽  
Exact Solutions ◽  
Linear Connection ◽  
Einstein Gravity ◽  
Matter Field ◽  
Einstein Equations ◽  
Deformation Method ◽  
Dimensional Gravity ◽  
Additional Constraints

We show how the Einstein equations with cosmological constant (and/or various types of matter field sources) can be integrated in a very general form following the anholonomic deformation method for constructing exact solutions in four- and five-dimensional gravity (S. Vacaru, IJGMMP 4 (2007) 1285). In this paper, we prove that such a geometric method can be used for constructing general non-Killing solutions. The key idea is to introduce an auxiliary linear connection which is also metric compatible and completely defined by the metric structure but contains some torsion terms induced nonholonomically by generic off-diagonal coefficients of metric. There are some classes of nonholonomic frames with respect to which the Einstein equations (for such an auxiliary connection) split into an integrable system of partial differential equations. We have to impose additional constraints on generating and integration functions in order to transform the auxiliary connection into the Levi-Civita one. This way, we extract general exact solutions (parametrized by generic off-diagonal metrics and depending on all coordinates) in Einstein gravity and five-dimensional extensions.

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