scholarly journals Applications of, and Extensions to, Selected Exact Solutions in General Relativity

2021 ◽  
Author(s):  
◽  
Bethan Cropp
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Bianchi Type ◽  
Plane Waves ◽  
Local Limit ◽  
Matter Content ◽  
Einstein Equations ◽  
Type I ◽  
Bianchi Type I ◽  
Stress Energy

<p>In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing down any arbitrary polarisation in this form. In addition to this we have extended this algorithm to an arbitrary number of dimensions, and have written down an explicit solution for a circularly polarized Rosen wave. In the second part a particular, ultra-local limit along an arbitrary timelike geodesic in any spacetime is constructed, in close analogy with the well-known lightlike Penrose limit. This limit results in a Bianchi type I spacetime. The properties of these spacetimes are examined in the context of this limit, including the Einstein equations, stress-energy conservation and Raychaudhuri equation. Furthermore the conditions for the Bianchi type I spacetime to be diagonal are explicitly set forward, and the effect of the limit on the matter content of a spacetime are examined.</p>

scholarly journals Applications of, and Extensions to, Selected Exact Solutions in General Relativity

2021 ◽  
Author(s):  
◽  
Bethan Cropp
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Bianchi Type ◽  
Plane Waves ◽  
Local Limit ◽  
Matter Content ◽  
Einstein Equations ◽  
Type I ◽  
Bianchi Type I ◽  
Stress Energy

<p>In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing down any arbitrary polarisation in this form. In addition to this we have extended this algorithm to an arbitrary number of dimensions, and have written down an explicit solution for a circularly polarized Rosen wave. In the second part a particular, ultra-local limit along an arbitrary timelike geodesic in any spacetime is constructed, in close analogy with the well-known lightlike Penrose limit. This limit results in a Bianchi type I spacetime. The properties of these spacetimes are examined in the context of this limit, including the Einstein equations, stress-energy conservation and Raychaudhuri equation. Furthermore the conditions for the Bianchi type I spacetime to be diagonal are explicitly set forward, and the effect of the limit on the matter content of a spacetime are examined.</p>

scholarly journals Classical Bianchi Type I Cosmology in K-Essence Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
J. Socorro ◽  
Luis O. Pimentel ◽  
Abraham Espinoza-García
Keyword(s):  
Cosmological Model ◽  
Cosmological Constant ◽  
Exact Solutions ◽  
Bianchi Type ◽  
Friedmann Equation ◽  
Matter Content ◽  
Type I ◽  
Bianchi Type I ◽  
Bianchi I ◽  
The Universe

We use one of the simplest forms of the K-essence theory and we apply it to the classical anisotropic Bianchi type I cosmological model, with a barotropic perfect fluid (p=γρ) modeling the usual matter content and with cosmological constantΛ. Classical exact solutions for anyγ≠1andΛ=0are found in closed form, whereas solutions forΛ≠0are found for particular values in the barotropic parameter. We present the possible isotropization of the cosmological model Bianchi I using the ratio between the anisotropic parameters and the volume of the universe. We also include a qualitative analysis of the analog of the Friedmann equation.

Energy–momentum distributions of Ruban universe in general relativity and teleparallel gravity

2019 ◽  
Vol 34 (03n04) ◽  
pp. 1950011 ◽  
Author(s):  
C. Aktaş
Keyword(s):  
General Relativity ◽  
Bianchi Type ◽  
Teleparallel Gravity ◽  
Type I ◽  
Universe Model ◽  
Zero Energy ◽  
Bianchi Type I ◽  
Momentum Distributions ◽  
Bianchi Type I Universe

In this study, we obtain Einstein, Bergmann–Thomson (BT), Landau–Lifshitz (LL), Møller, Papapetrou (PP) and Tolman energy–momentum (EM) distributions for Ruban universe model in general relativity (GR) and teleparallel gravity (TG). We obtain same results for Einstein, Bergmann–Thomson and Landau–Lifshitz energy–momentum distributions in GR and TG. Also, we get same results for Einstein and Tolman energy–momentum distributions in GR. The Møller energy–momentum results are different in GR and TG. Also, using Ruban universe model, we obtain LRS Bianchi type I solutions and we get zero energy–momentum results for this universe model in GR and TG. These results of LRS Bianchi type I universe model agree with Aygün et al., Taşer et al., Doğru et al., Banerjee–Sen, Tryon and Xulu in different gravitation theories.

scholarly journals LRS BIANCHI TYPE-I COSMOLOGICAL MODELS IN BARBER'S SECOND SELF CREATION THEORY

2002 ◽  
Vol 11 (08) ◽  
pp. 1195-1207 ◽  
Author(s):  
ANIRUDH PRADHAN ◽  
ANIL KUMAR VISHWAKARMA
Keyword(s):  
Physical Properties ◽  
Exact Solutions ◽  
Perfect Fluid ◽  
Deceleration Parameter ◽  
Bianchi Type ◽  
Cosmological Models ◽  
Type I ◽  
Fluid Source ◽  
Bianchi Type I ◽  
Radiation Universe

Barber's second self creation theory with perfect fluid source for an LRS Bianchi type-I metric is considered using deceleration parameter to be constant where the metric potentials are taken as functions of x and t. In particular, some exact solutions have also been obtained for the vacuum universe, Zel'dovich universe and radiation universe. Some physical properties of the models are also discussed.

Homothetic vector field in plane symmetric Bianchi type-I cosmological model in Lyra geometry

2014 ◽  
Vol 29 (22) ◽  
pp. 1450116 ◽  
Author(s):  
Ragab M. Gad ◽  
A. S. Alofi
Keyword(s):  
General Relativity ◽  
Vector Field ◽  
Riemannian Geometry ◽  
Bianchi Type ◽  
Displacement Vector ◽  
Lyra Geometry ◽  
Type I ◽  
Bianchi Type I ◽  
Plane Symmetric ◽  
Homothetic Vector

In this paper, we obtain a homothetic vector field of a plane symmetric Bianchi type-I spacetime based on Lyra geometry. We discuss the cases when the displacement vector is function of t and when it is constant. We investigate the equation of state in both two cases. A comparison between the obtained results, using Lyra geometry, and that have obtained previously in the context of General Relativity (GR), based on Riemannian geometry, will be given.

CLASSIFICATION OF BIANCHI TYPE I SPACETIMES ACCORDING TO THEIR PROPER TELEPARALLEL HOMOTHETIC VECTOR FIELDS IN THE TELEPARALLEL THEORY OF GRAVITATION

2010 ◽  
Vol 25 (25) ◽  
pp. 2145-2153 ◽  
Author(s):  
GHULAM SHABBIR ◽  
SUHAIL KHAN
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Bianchi Type ◽  
Special Choice ◽  
Type I ◽  
Bianchi Type I ◽  
Homothetic Vector ◽  
Teleparallel Theory ◽  
Theory Of Gravitation

In this paper we explored teleparallel homothetic vector fields in Bianchi type I spacetimes in the teleparallel theory of gravitation using direct integration technique. It turns out that the dimensions of the teleparallel homothetic vector fields are 4, 5, 7 or 11 which are same in numbers as in general relativity. In the cases of 4, 5 or 7 proper teleparallel homothetic vector fields exist for the special choice of the spacetimes. In the case of 11 teleparallel homothetic vector fields all the torsion components are zero. The homothetic vector fields of general relativity are recovered in this case and the spacetime become Minkowski.

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