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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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01 Jan 1962
14 citations
14 citations
TL;DR: In this paper, it was shown that if a solution of the Weyl equation in some Riemann space is asymptotically smooth and describes a neutrino field with causal behaviour, than the order of the radiation term in the corresponding energy-momentum tensor predominates asymptonically the orders of the other terms.
Abstract: It is shown that, if a solution of the Weyl equation in some Riemann space is asymptotically smooth and describes a neutrino field with causal behaviour, than the order of the radiation term in the corresponding energy-momentum tensor predominates asymptotically the orders of the other terms.
14 citations
TL;DR: In this paper, the authors examine the claim of Babak and Grishchuk to have solved the problem of localizing the energy and momentum of the gravitational field and conclude that this object has no physical significance.
Abstract: We examine the claim of Babak and Grishchuk [S. V. Babak and L. P. Grishchuk, Phys. Rev. D 61, 024038 (1999)] to have solved the problem of localizing the energy and momentum of the gravitational field. After summarizing Grishchuk's flat-space formulation of gravity, we demonstrate its equivalence to general relativity at the level of the action. Two important transformations are described (diffeomorphisms applied to all fields, and diffeomorphisms applied to the flat-space metric alone) and we argue that both should be considered gauge transformations: they alter the mathematical representation of a physical system, but not the system itself. By examining the transformation properties of the Babak-Grishchuk gravitational energy-momentum tensor under these gauge transformations (infinitesimal and finite) we conclude that this object has no physical significance.
14 citations
TL;DR: In this article, an attempt is made to clarify the physical and the mathematical reasonings that underlie Einstein's laws of gravitation, and it appears that only by a mixture of physical reasonableness, mathematical simplicity, and aesthetic sensibility can one arrive at Einstein's field equations.
Abstract: An attempt is made to clarify the physical and the mathematical reasonings that underlie Einstein's laws of gravitation. It appears that only by a mixture of physical reasonableness, mathematical simplicity, and aesthetic sensibility can one arrive at Einstein's field equations. The general theory of relativity is in fact an example of “the power of speculative thought.” The topics considered include a discussion of the principle of equivalence and the view of space-time as a geometric manifold. Two “derivations” of Einstein's equations are given: one based on physical reasonableness and the other based on a variational principle and mathematical simplicity.
14 citations