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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 general framework for the analysis of high-order nonspherical perturbations of a four-dimensional spherical spacetime by including a gauge-invariant description of the perturbation is presented.
Abstract: We complete the formulation of a general framework for the analysis of high-order nonspherical perturbations of a four-dimensional spherical spacetime by including a gauge-invariant description of the perturbations. We present a general algorithm to construct these invariants and provide explicit formulas for the case of second-order metric perturbations. We show that the well-known problem of lack of invariance for the first-order perturbations with $l=0$, 1 propagates to increasing values of $l$ for perturbations of higher order, owing to mode coupling. We also discuss in which circumstances it is possible to construct the invariants.
23 citations
TL;DR: In this article, a slice theorem for the action of Diff on the space of solutions of the Einstein equations in the asymptotically flat case is proved, which is the case in which we are interested in this paper.
23 citations
TL;DR: In this article, the spin-gravity-electromagnetism coupling is investigated for motion in the background of a Reissner-Nordstrom black hole both in the exact spacetime and in the weak-field approximation.
Abstract: The dynamics of a charged spinning test particle in general relativity is studied in the context of gravitoelectromagnetism. Various families of test observers and supplementary conditions are examined. The spin-gravity-electromagnetism coupling is investigated for motion in the background of a Reissner-Nordstr\"om black hole both in the exact spacetime and in the weak-field approximation. Results are compared with those of the theory.
23 citations
01 Jan 2005
TL;DR: A comprehensive overview of the final version of the general theory of relativity can be found in this paper, which includes a self-contained exposition of the elements of tensor calculus that are needed for the theory.
Abstract: Publisher Summary This chapter discusses Albert Einstein's reviews paper on general relativity theory. This paper was the first comprehensive overview of the final version of Einstein's general theory of relativity after several expositions of preliminary versions and latest revisions of the theory in November 1915. It includes a self-contained exposition of the elements of tensor calculus that are needed for the theory. It presented a conceptual analysis of the notions of space and time, with a critical reassessment of the meaning of simultaneity at its core. Its most salient features are length contraction and time dilation in a system that is in uniform relative motion to an observer with a speed comparable to that of light. Einstein concluded that generally covariant field equations cannot uniquely determine the physical processes in a gravitational field. Consequently, there had to be restriction of the admissible coordinate systems to what he began to call “adapted coordinates.” Einstein tried to encourage experimental efforts aimed at testing the two main predictions of the theory. A confirmation of the gravitational red shift was difficult to determine because of the many competing effects that result in a shifting or broadening of solar or stellar spectral lines.
22 citations
TL;DR: Solutions of the combined gravitational and mesic fields are attempted in this article, where the mesic field cannot be solved in strictly empty space, it is solved for non-empty space.
Abstract: Solutions of the combined gravitational and mesic fields are attempted. Since the mesic field cannot be solved in strictly empty space, it is solved for nonempty space. (D.L.C.)
22 citations