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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: It is found that such a generalized Einstein action must include at least one scalar field and one vector field as well as the quadratic term of the scalar curvature.
Abstract: We study a generalized Einstein theory with the following two criteria: (i) on the solar scale, it must be consistent with the classical tests of general relativity; (ii) on the galactic scale, the gravitational potential is a sum of Newtonian and Yukawa potentials so that it may explain the flat rotation curves of spiral galaxies. Under these criteria we find that such a generalized Einstein action must include at least one scalar field and one vector field as well as the quadratic term of the scalar curvature.
10 citations
TL;DR: In this paper, the exact Schwarzschild and Reissner Nordstrom solutions are investigated in detail, and the results are compared with those in the recent work by J. D. Brown and J. W. York.
Abstract: The problems of the tolal energy and quasilocalenergy density or an isolated spherically symmetric static system in general relativity (GR) are considered with examples of some exact suintions. The field formulation of GR dereloped earlier hy L. P. Grishchuk. el al. (1984). in ihe framework of which all the dynamical fields, including the gravitation field, are considered in a fixed background spacetime is used intensively. The exact Schwarzschild and Reissner Nordstrom solutions are investigated in detail, and the results are compared with those in the recent work by J. D. Brown and J. W. York. Jr. (1993) as well as discussed with respect to the principle of nonlocalization of the gravitational energy in GR. Those examples are illustrative and simple because the background is selected as Minkowski spacetime and, in fact, the field configurations are studied in the framework of special relativity. It is shown that some problems of the Schwarzschild solution which are difficult to resolve in the standard geometrical framework of GR are resolved in the framework of the field formulation.
10 citations
TL;DR: In this article, a cosmological model based on general relativity with non vanishing divergence for the energy-momentum tensor is consistent with the observed values for the nucleosynthesis of helium for some values of the arbitrary parameter presented in this model.
Abstract: We show that a previously proposed cosmological model based on general relativity with non vanishing divergence for the energy-momentum tensor is consistent with the observed values for the nucleosynthesis of helium for some values of the arbitrary parameter $\alpha$ presented in this model. Further more values of $\alpha$ can be accommodated if we adopt the Randall-Sundrum single brane model.
10 citations
10 citations
TL;DR: In this article, it was shown that a static solution of the Einstein equations inside an infinite plate of an ideal liquid with continuous metric coefficients and their first derivatives cannot have a plane of mirror symmetry.
Abstract: It is shown that a static solution of the Einstein equations inside an infinite plate of an ideal liquid with continuous metric coefficients and their first derivatives cannot have a plane of mirror symmetry. As a consequence, the boundaries of the plate are joined with qualitatively different vacuum solutions on both sides of the plate.
10 citations