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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, the field equations of general relativity are applied to pressure-free spherically symmetrical systemsof particles and the equations of motion are determined without the use of approximations and are compared with the Newtonian equations.
Abstract: The field equations of general relativity areapplied to pressure-free spherically symmetrical systemsof particles. The equations of motion are determinedwithout the use of approximations and are compared with the Newtonian equations. The total energyis found to be an important parameter, determining thegeometry of 3-space and the ratio of effectivegravitating to invariant mass. The Doppler shift isdiscussed and is found to contain both the velocity shiftand the Einstein shift combined in a rather complexexpression.
811 citations
TL;DR: In this paper, a set of covariant conservation laws is constructed in the general theory of relativity, and their relationship to the generators of infinitesimal coordinate transformations is indicated.
Abstract: A set of covariant conservation laws is constructed in the general theory of relativity. Their relationship to the generators of infinitesimal coordinate transformations is indicated. In a given coordinate system certain of these quantities may be naturally identified as energy and momentum. We can continue to recognize these conserved quantities in all coordinate systems due to the covariant character of the expressions.
793 citations
768 citations
TL;DR: In this article, a concluding review exposition of the investigations aimed at the construction of a general cosmological solution of the Einstein equations with a singularity in time is presented, which is a continuation of the previous (1970) paper by the authors in this Journal.
Abstract: This paper is a concluding review exposition of the investigations aimed at the construction of a general cosmological solution of the Einstein equations with a singularity in time; thus it is a direct continuation of the previous (1970) paper by the authors in this Journal. A detailed description is given of the analysis which leads to the construction of such a solution, and of its properties.
707 citations
TL;DR: In this paper, a method is described for constructing, from any source-free solution of Einstein's equations which possesses a Killing vector, a one-parameter family of new solutions.
Abstract: A method is described for constructing, from any source‐free solution of Einstein's equations which possesses a Killing vector, a one‐parameter family of new solutions. The group properties of this transformation are discussed. A new formalism is given for treating space‐times having a Killing vector.
682 citations