New class of regular and well behaved exact solutions in general relativity

2010 ◽  
Vol 330 (2) ◽  
pp. 353-359 ◽  
Author(s):  
Neeraj Pant ◽  
R. N. Mehta ◽  
Mamta Joshi Pant
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
New Class

scholarly journals Breaking the cosmological background degeneracy by two-fluid perturbations in f(R) gravity

2015 ◽  
Vol 24 (07) ◽  
pp. 1550053 ◽  
Author(s):  
Amare Abebe
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Structure Formation ◽  
Background Level ◽  
Cosmological Perturbations ◽  
Gauge Invariant ◽  
First Order ◽  
Cosmological Background ◽  
Theories Of Gravity ◽  
Two Fluid

One of the exact solutions of f(R) theories of gravity in the presence of different forms of matter exactly mimics the ΛCDM solution of general relativity (GR) at the background level. In this work we study the evolution of scalar cosmological perturbations in the covariant and gauge-invariant formalism and show that although the background in such a model is indistinguishable from the standard ΛCDM cosmology, this degeneracy is broken at the level of first-order perturbations. This is done by predicting different rates of structure formation in ΛCDM and the f(R) model both in the complete and quasi-static regimes.

GEOMETRIC INTEGRATION BY SOLUTION INTERPOLATION

2009 ◽  
Vol 20 (02) ◽  
pp. 313-322
Author(s):  
PILWON KIM
Keyword(s):  
Differential Equation ◽  
Heat Equation ◽  
Exact Solutions ◽  
Standard Method ◽  
Interpolation Method ◽  
Nonlinear Heat Equation ◽  
Geometric Integration ◽  
Numerical Schemes ◽  
New Class ◽  
Geometric Integrators

Numerical schemes that are implemented by interpolation of exact solutions to a differential equation naturally preserve geometric properties of the differential equation. The solution interpolation method can be used for development of a new class of geometric integrators, which generally show better performances than standard method both quantitatively and qualitatively. Several examples including a linear convection equation and a nonlinear heat equation are included.

New class of exact solutions of the Dirac equation

1975 ◽  
Vol 16 (10) ◽  
pp. 2089-2092 ◽  
Author(s):  
Franklin S. Felber ◽  
John H. Marburger
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
New Class

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.

A new class of exact solutions of the Vlasov equation

2001 ◽  
Vol 8 (12) ◽  
pp. 5081-5085 ◽  
Author(s):  
M. Y. Yu ◽  
Zhaoyang Chen ◽  
L. Stenflo
Keyword(s):  
Exact Solutions ◽  
Vlasov Equation ◽  
New Class

Some exact anisotropic solutions in general relativity

1984 ◽  
Vol 62 (3) ◽  
pp. 239-246 ◽  
Author(s):  
K. D. Krori ◽  
P. Borgohain ◽  
Ranjumani Devi
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Anisotropic Matter ◽  
Degree Of Anisotropy ◽  
Range Of Values ◽  
Suitable Modification

Some exact solutions for anisotropic matter are worked out in the framework of general relativity. Four such solutions are obtained by a suitable modification of four well-known solutions by Tolman, viz., Tolman's solutions III, IV, V, and VI. The degree of anisotropy is determined by a parameter, and the range of values this parameter will have under realistic situations is calculated for all four classes. A singularity-free new solution for anisotropic matter is also presented.

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