scholarly journals Finding and using exact solutions of the Einstein equations

2006 ◽  
Author(s):  
M. A. H. MacCallum
Keyword(s):  
Exact Solutions ◽  
Einstein Equations

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 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 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.

scholarly journals HORIZONS AND GEODESICS OF BLACK ELLIPSOIDS

2003 ◽  
Vol 12 (03) ◽  
pp. 479-494 ◽  
Author(s):  
SERGIU I. VACARU
Keyword(s):  
Exact Solutions ◽  
Einstein Equations ◽  
Analytic Extension ◽  
Vacuum Einstein Equations ◽  
Geodesic Structure ◽  
Small Deformations

We analyze the horizon and geodesic structure of a class of 4D off–diagonal metrics with deformed spherical symmetries, which are exact solutions of the vacuum Einstein equations with anholonomic variables. The maximal analytic extension of the ellipsoid type metrics are constructed and the Penrose diagrams are analyzed with respect to the adapted frames. We prove that for small deformations (small eccentricities) there are such metrics that the geodesic behaviour is similar to the Schwarzcshild one. We conclude that some vacuum static and stationary ellipsoid configurations1,2 may describe black ellipsoid objects.

scholarly journals Nondiffracting gravitational waves

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
Felipe A. Asenjo ◽  
Sergio A. Hojman
Keyword(s):  
Exact Solutions ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Wave Packets ◽  
Einstein Equations ◽  
Airy Functions ◽  
Linearized Gravity

AbstractIt is proved that accelerating nondiffracting gravitational Airy wave-packets are solutions of linearized gravity. It is also showed that Airy functions are exact solutions to Einstein equations for non-accelerating nondiffracting gravitational wave-packets.

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