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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, a general equation for the rate of change of the total energy of a sphere in a spherically symmetric distribution of charged matter is derived for the case of a spheroid.
Abstract: The Einstein–Maxwell equations for a spherically symmetric distribution of charged matter are studied. A general equation is derived for the rate of change of the "total energy" of the sphere in te...
34 citations
TL;DR: In this paper, a method for obtaining general relations governing the behavior of magnetofluids in general relativity is presented, and their possible relevance to galactic cosmogony, gravitational collapse, and pulsar theory is briefly discussed.
Abstract: A method is outlined for obtaining general relations governing the behavior of magnetofluids in general relativity. Several such relations are obtained for the case of infinite conductivity, and their possible relevance to galactic cosmogony, gravitational collapse, and pulsar theory is briefly discussed.
34 citations
01 Jan 1991
TL;DR: In this paper, the Lagrangian approach to conserved currents in field theories is discussed and the results apply to general relativity and to relativistic field theories and the fundamental theory of conserved quantities associated to the gravitational field itself is discussed.
Abstract: Publisher Summary This chapter reviews general ideas and results concerning the geometric “Lagrangian” approach to conserved currents in field theories and shows how these results apply to general relativity and to relativistic field theories. Although general relativity is a well-established theory of gravity interacting with external matter, there is still no general agreement on the definition of mass and of conserved quantities associated to the gravitational field itself. The chapter reviews the fundamentals of the theory of conserved quantities as it follows from the Poincare–Cartan form approach to the higher-order calculus of variations. It further analyzes the interaction between matter fields and gravitation, the first-order covariant formulation of general relativity, and the field theories on a fixed background.
34 citations
TL;DR: In this article, a generalization of the Lanczos equation for the presence of signature change using variational methods is presented. But the authors only consider the case when the extrinsic curvature is continuous.
Abstract: We discuss Einstein’s field equations in the presence of signature change using variational methods, obtaining a generalization of the Lanczos equation relating the distributional term in the stress tensor to the discontinuity of the extrinsic curvature. In particular, there is no distributional term in the stress tensor, and hence no surface layer, precisely when the extrinsic curvature is continuous, in agreement with the standard result for constant signature.
34 citations
TL;DR: Einstein regarded as one of the triumphs of his 1915 theory of gravity -the general theory of relativity -that it vindicated the action-reaction principle, while Newtonian mechanics as well as his 1905 special theory of general relativity supposedly violated it as mentioned in this paper.
Abstract: Einstein regarded as one of the triumphs of his 1915 theory of gravity - the general theory of relativity - that it vindicated the action-reaction principle, while Newtonian mechanics as well as his 1905 special theory of relativity supposedly violated it. In this paper we examine why Einstein came to emphasise this position several years after the development of general relativity. Several key considerations are relevant to the story: the connection Einstein originally saw between Mach's analysis of inertia and both the equivalence principle and the principle of general covariance, the waning of Mach's influence owing to de Sitter's 1917 results, and Einstein's detailed correspondence with Moritz Schlick in 1920.
34 citations