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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, a complete set of solutions of the field equations with Tij = (e + p)uiuj − pgij is found, and they divide into three families, first of which contains six types of new solutions with nonzero pressure.
Abstract: The equations of isentropic rotational motion of a perfect fluid are investigated with use of Darboux’ theorem. It is shown that, together with the equation of continuity, they guarantee the existence of four scalar functions on space−time, which constitute a dynamically distinguished set of coordinates. It is assumed that in this coordinate system the metric tensor is constant along the lines tangent to velocity and vorticity fields. Under these assumptions a complete set of solutions of the field equations with Tij = (e + p)uiuj − pgij is found. They divide into three families, first of which contains six types of new solutions with nonzero pressure. The second family contains only the Godel’s solution, and the third one, only the Lanczos’ solution. Symmetry groups, exterior metrics, type of conformal curvature, geometrical and physical properties of the new solutions are investigated. A short review of other models of rotating matter is given.
31 citations
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TL;DR: Bilaniuk and Sudarshan as discussed by the authors argued that valid solutions of Albert Einstein's relativity equations describe faster-than-light particles called "tachyons" and that tachyons must exist.
Abstract: “Anything that is not forbidden is compulsory,” says Murray Gell-Mann's half-facetious totalitarian principle. What then about faster-than-light particles called “tachyons”? In their May article Olexa-Myron Bilaniuk and E. C. George Sudarshan argued that valid solutions of Albert Einstein's relativity equations describe such particles. Thus if Einstein's equations are accurate descriptions of the physical universe and if solutions not forbidden are compulsory, tachyons must exist.
31 citations
30 citations
30 citations
TL;DR: In this paper, the correlation tensor in a Friedmann-lema-tre-Robertson-Walker (FLRW) background is found to be of the form of a spatial curvature.
Abstract: We discuss the averaging problem in general relativity, using the form of the macroscopic gravity equations in the case of spherical symmetry in volume preserving coordinates. In particular, we calculate the form of the correlation tensor under some reasonable assumptions on the form for the inhomogeneous gravitational field and matter distribution. On cosmological scales, the correlation tensor in a Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) background is found to be of the form of a spatial curvature. On astrophysical scales the correlation tensor can be interpreted as the sum of a spatial curvature and an anisotropic fluid. We briefly discuss the physical implications of these results.
30 citations