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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 article, the Lense-Thirring precession was derived from the equations of general relativity, assuming that the particles are slowly moving (v≪c), and the gravitational field is sufficiently weak that nonlinear terms in Einstein's field equations can be neglected.
Abstract: Starting from the equations of general relativity, equations similar to those of electromagnetic theory are derived. It is assumed that the particles are slowly moving (v≪c), and the gravitational field is sufficiently weak that nonlinear terms in Einstein’s field equations can be neglected. For static fields, the analogy to electrostatics and magnetostatics is very close. Results are compared with those of a previous derivation by Braginsky, Caves, and Thorne [Phys. Rev. D 15, 2047–2068 (1977)]. These results lead to very simple derivations of the Lense–Thirring precession [Phys. Z. 19, 156–163 (1918)] and the spin‐curvature force of Papepetrou [Proc. R. Soc. London Ser. A 209, 248–258 (1951)] and Pirani [Acta Phys. Pol. 15, 389–405 (1956)].
78 citations
TL;DR: In this paper, the authors provide a fairly concise introduction to the basic mathematical concepts of the general theory of relativity and their applications, at a level suitable for postgraduate students, covering Riemannian geometry and Einstein's theory of gravitation, gravitational waves, the classification of exact solutions of the Einstein equations, black holes and cosmology.
Abstract: Hans Stephani 1982 Cambridge: Cambridge University Press xvi + 298 pp price £25 This textbook provides a fairly concise introduction to the basic mathematical concepts of the general theory of relativity and their applications, at a level suitable for postgraduate students. It covers Riemannian geometry and Einstein's theory of gravitation, gravitational waves, the classification of exact solutions of the Einstein equations, black holes and cosmology.
78 citations
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TL;DR: In this paper, the fundamentals of the teleparallel equivalent of general relativity are presented, and its main properties described, including the field equations, the definition of an energy-momentum density for the gravitational field, the tele-parallel version of the equivalence principle, and the dynamical role played by torsion as compared to the corresponding role playing by curvature in general relativity.
Abstract: The fundamentals of the teleparallel equivalent of general relativity are presented, and its main properties described. In particular, the field equations, the definition of an energy--momentum density for the gravitational field, the teleparallel version of the equivalence principle, and the dynamical role played by torsion as compared to the corresponding role played by curvature in general relativity, are discussed in some details.
76 citations
TL;DR: In this article, the energy-momentum tensor of the gravitational field is identified in the teleparallel equivalent of general relativity and the spatial components of this tensor yield a consistent definition of the gravity pressure.
Abstract: In the framework of the teleparallel equivalent of general relativity it is possible to establish the energy-momentum tensor of the gravitational field. This tensor has the following essential properties: (1) it is identified directly in Einstein's field equations; (2) it is conserved and traceless; (3) it yields expressions for the energy and momentum of the gravitational field; (4) is is free of second (and highest) derivatives of the field variables; (5) the gravitational and matter energy-momentum tensors take place in the field equations on the same footing; (6) it is unique. However it is not symmetric. We show that the spatial components of this tensor yield a consistent definition of the gravitational pressure.
75 citations
TL;DR: For isolated gravitating systems of physical interest, the difference between the Arnowitt-Deser-Misner four-momentum and the Bondi four-moverment associated with a retarded instant of time was shown to equal the four momentum carried away by the gravitational radiation emitted between infinite past and the given retarded instant.
Abstract: For isolated gravitating systems of physical interest, the difference between the Arnowitt-Deser-Misner four-momentum and the Bondi four-momentum associated with a retarded instant of time is shown to equal the four-momentum carried away by the gravitational radiation emitted between infinite past and the given retarded instant.
75 citations