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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, an analogy between the Lienard-Wiechert solutions of the Maxwell equations and the Robinson-Trautman solution of the Einstein equations was established by virtue of the fact that a principal null vector field of either the Maxwell or Weyl tensor in each case satisfies the following four conditions: (1) the field is a geodesic field, (2) it has non-vanishing divergence, (3) it is shear free, and (4) twist (or curl) free.
Abstract: An analogy is established between the Lienard‐Wiechert solutions of the Maxwell equations and the Robinson‐Trautman solutions of the Einstein equations by virtue of the fact that a principal null vector field of either the Maxwell or Weyl tensor in each case satisfies the following four conditions: (1) The field is a geodesic field, (2) it has nonvanishing divergence, (3) it is shear free, and (4) it is twist (or curl) free.

25 citations

Journal ArticleDOI
TL;DR: In this paper, it is shown that the Noether stress energy tensor is equivalent to the gravitational tensor for general matter fields under the influence of gravity, and the full equivalence is established for matter fields that do not couple to the metric derivatives.
Abstract: It is dealt with the question, under which circumstances the canonical Noether stress-energy tensor is equivalent to the gravitational (Hilbert) tensor for general matter fields under the influence of gravity. In the framework of general relativity, the full equivalence is established for matter fields that do not couple to the metric derivatives. Spinor fields are included into our analysis by reformulating general relativity in terms of tetrad fields, and the case of Poincare gauge theory, with an additional, independent Lorentz connection, is also investigated. Special attention is given to the flat limit, focusing on the expressions for the matter field energy (Hamiltonian). The Dirac-Maxwell system is investigated in detail, with special care given to the separation of free (kinetic) and interaction (or potential) energy. Moreover, the stress-energy tensor of the gravitational field itself is briefly discussed.

25 citations

Journal ArticleDOI
TL;DR: In this paper, a class of modified gravity theories that deform general relativity in a way that breaks time reversal invariance and, very mildly, locality are described. But the algebra of constraints, local physical degrees of freedom, and their linearized equations of motion are unchanged, yet observable effects may be present on cosmological scales, which have implications for the early history of the universe.
Abstract: We describe a class of modified gravity theories that deform general relativity in a way that breaks time reversal invariance and, very mildly, locality. The algebra of constraints, local physical degrees of freedom, and their linearized equations of motion, are unchanged, yet observable effects may be present on cosmological scales, which have implications for the early history of the universe. This is achieved in the Hamiltonian framework, in a way that requires the constant mean curvature gauge conditions and is, hence, inspired by shape dynamics.

25 citations

Journal Article
TL;DR: In this article, the authors develop from a variational formulation the field equations, jump conditions across a discontinuity surface and nonlinear constitutive equations for a magnetized elastic medium with finite deformations in the frame of the general theory of relativity.
Abstract: In this article, we develop from a variational formulation the field equations, jump conditions across a discontinuity surface and nonlinear constitutive equations for a magnetized elastic medium with finite deformations in the frame of the general theory of relativity. RESUME. Dans le present article, nous généralisons dans le cadre de la relativité générale, la théorie des milieux continus déformables en interaction avec le champ magnétique donnée precedemment dans le cadre de la relativité restreinte [6][25]-[27]. Le milieu continu considéré est un milieu solide élastique sujet a des deformations finies et en interaction avec les champs gravifique et magnétique. Un principe variationnel qui suit la formulation que Taub [12] a donnée pour le schema fluide parfait est employe. Toutes les equations du champ (equations d’Einstein, conservation de 1’impulsion-energie, equations de Maxwell dans un milieu matériel, conservation du flux d’entropie) en découlent ainsi que les conditions de saut a travers une surface de discontinuité. Comme dans le travail de Taub, il est montré que cette derniere ne peut etre variée indépendamment du parametre thermodynamique. Les lois non-linéaires de comportement sont également obtenues a partir d’un potentiel, l’énergie libre de Helmholtz qui est écrite sous forme invariante, ceci généralisant la contrainte habituellement imposée par le principe d’indifference matérielle en mécanique classique des milieux continus. ANN. INST. POINCARÉ, A-X V-4 20 276 G~RARD A. MAUGIN

25 citations

Journal ArticleDOI
TL;DR: In this paper, the energy distribution associated with a static spherically symmetric non-singular phantom black hole metric in general relativity was calculated in quasi-Cartesian coordinates.
Abstract: We calculate the energy distribution associated with a static spherically symmetric non-singular phantom black hole metric in Einstein's prescription in general relativity. As required for the Einstein energy-momentum complex, we perform the calculations in quasi-Cartesian coordinates. We also calculate the momentum components and obtain a zero value, as expected from the geometry of the metric.

25 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20232
20226
20191
20185
201734
201662