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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 vacuum field equations are integrated in complex relativity in a major subcase of the class whose Weyl tensor is of the type N⊗N, i.e., when the left and right Weyl spinors are each of typeN.
Abstract: Einstein's vacuum field equations are integrated in complex relativity in a major subcase of the class whose Weyl tensor is of the type N⊗N, ie, when the left and right Weyl spinors Ψ and\(\tilde \Psi \) are each of typeN The subcase is the complex equivalent of the real nontwisting case Five separate families of solutions are found Three of these are complexified versions of the two families of plane-fronted waves and the Robinson-Trautman real type-N metrics and two are complex solutions which do not have any real slices of Lorentz signature Before the equations are integrated, the relevant general theory and equations are developed in a tetrad frame which is well suited to the discussion of these and a wider class of complex solutions and is called aleft quarter flat frame The relationship between this frame and the coordinates used and some other frames and coordinates, including the complexified version of the frame often used for real type-N metrics, is discussed
12 citations
TL;DR: In this paper, it was shown that the intermediate singularities become localized curvature singularities while the Cauchy horizons are a stable feature of the models and that scalar-wave propagation in these spaces is possible.
Abstract: It has been shown that "intermediate" singularities, where all Riemann tensor invariants are finite, occur in certain cosmological models. Associated with the singularities are Cauchy horizons, across which the matter flows into a stationary region of space-time. We investigate scalar-wave propagation in these spaces. Our results suggest that the intermediate singularities become localized curvature singularities while the Cauchy horizons are a stable feature of the models.
12 citations
TL;DR: The geometric structure equations of a manifold satisfying the vacuum Einstein equations are expressed in terms of a complexification of the space of 2-forms adapted to the Petrov classification as discussed by the authors.
Abstract: The geometric structure equations of a manifold satisfying the vacuum Einstein equations are expressed in terms of a complexification of the space of 2‐forms adapted to the Petrov classification. The Petrov type III problem is invariantly reduced to the solution of one partial differential equation. Examples of solutions containing one arbitrary function are given, corresponding to spaces with groups of motions of dimensions 0, 1, and 2.
12 citations
TL;DR: In this article, the authors verified the consistency of the energy-momentum and angular momentum tensor of the gravitational field established in the Hamiltonian structure of the Teleparallel Equivalent of General Relativity (TEGR) in the closed universe of the Friedmann-Lemaitre-Robertson-Walker (FLRW).
Abstract: The main purpose of this paper is to explicitly verify the consistency of the energy-momentum and angular momentum tensor of the gravitational field established in the Hamiltonian structure of the Teleparallel Equivalent of General Relativity (TEGR). In order to reach these objectives, we obtained the total energy and angular momentum (matter plus gravitational field) of the closed universe of the Friedmann-Lemaitre-Robertson-Walker (FLRW). The result is compared with those obtained from the pseudotensors of Einstein and Landau-Lifshitz. We also applied the field equations (TEGR) in an expanding FLRW universe. Considering the stress energy-momentum tensor for a perfect fluid, we found a teleparallel equivalent of Friedmann equations of General Relativity (GR).
12 citations
12 citations