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Introduction to the mathematics of general relativity
About: Introduction to the mathematics of general relativity is a research topic. Over the lifetime, 2583 publications have been published within this topic receiving 73295 citations.
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TL;DR: In this paper, a solution having spherical symmetry for the generalized field theory established recently by Mikhail and Wanas, based on the tetrad space, is obtained, and it is shown that the solution obtained represents a pure gravitational field outside a spherically symmetric body.
Abstract: A solution having spherical symmetry for the generalized field theory established recently by Mikhail and Wanas, based on the tetrad space, is obtained. The field equations of general relativity, in free space and written in terms of the tetrad elements, are solved also by using the same tetrad field. The solution obtained from the new theory is found to be identical with that obtained from general relativity. It is shown that the solution obtained represents a pure gravitational field outside a spherically symmetric body. It is found that the new theory, in the absence of electromagnetic field and when the gravitational field is not strong, gives the same results of general relativity in the case of spherical symmetry. This result supports the idea of classification of tetrad vector fields, presented in a recent paper.
10 citations
TL;DR: In this paper, it was shown that for a spherically symmetric perfect fluid solution to be of class one, either (i) e = 0, or (ii) e+R=0,e andR being respectively the eigenvalue of the Weyl tensor in Petrov's classification and spur of the Ricci tensor.
Abstract: It is shown that for a spherically symmetric perfect fluid solution to be of class one, either (i) e=0, or (ii) e+R=0,e andR being respectively the eigenvalue of the Weyl tensor in Petrov's classification and spur of the Ricci tensor. Hence, it is deduced that whereas every conformally flat perfect fluid solution is of class one, the converse is not true in general. However, the converse does hold for all solutions withρ=3p.
10 citations
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TL;DR: In this paper, a fully covariant energy momentum stress tensor for the gravitational field is given, which is easily physically motivated and leads to a general derivation of the Einstein equation for gravity.
Abstract: We give a fully covariant energy momentum stress tensor for the gravitational field which is easily physically motivated, and which leads to a very general derivation of the Einstein equation for gravity. We do not need to assume any property of the surce matter fields' energy momentum stress tensor other than symmetry. We give a physical motivation for this choice using laser light pressure. As a consequence of our derivation, the energy momentum stress tensor for the total source matter and fields must be divergence free, when spacetime is 4 dimensional. Moreoverr, if the total source matter fields are assumed to be divergence free, then either spacetime is dimension 4 or the spacetime has constant scalar curvature.
10 citations
01 Jan 1977
10 citations
10 citations