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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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Journal ArticleDOI
TL;DR: In this paper, the authors extended the existing 4-dimensional relativity by extending it to the 6-dimensional conformal (ηa)-space (flat or curved one) with the metric tensorgab (a, b=0, 1, 2, 3, 5, 6), where all components of the 6vector ηa=(ημ=κxμ, κ, λ) are considered as independent physical degrees of freedom.
Abstract: We have done a «mininal» change in the existing 4-dimensional relativity, by extending it to the 6-dimensional conformal (ηa)-space (flat or curved one) with the metric tensorgab (a, b=0, 1, 2, 3, 5, 6), where all components of the 6-vector ηa=(ημ=κxμ, κ, λ) are considered as independent physical degrees of freedom. All basic equations of (special and general) relativity in 6-dimensional (flat or curved) conformal (ηa)-space have the same form as the corresponding equations in the 4-dimensional space. The novel feature of such an extended theory (named «conformal relativity») is the introduction of thescale degree of freedom κ, which can be different from 1 and can change along the particle world-line. However, if κ=1 (\(\dot \kappa = 0\)), then the conformal relativity reduces to the usual, 4-dimensional relativity. Geodesics in the curved (ηa)-space correspond to the motion of electrically charged test partcles in gravitational and/or electromagnetic fields. The field equations for the metric tensorgab are Einstein equations, extended to the (ηa)-space; they describe a gravitational and electromagnetic field.

17 citations

Posted Content
TL;DR: In this article, different topos-theoretical approaches to the problem of construction of General Theory of Relativity (GOR) have been studied, and a new theory of space-time, created in a purely logical manner, has been proposed.
Abstract: We study in this paper different topos-theoretical approaches to the problem of construction of General Theory of Relativity. In general case the resulting space-time theory will be non-classical, different from that of the usual Einstein theory of space-time. This is a new theory of space-time, created in a purely logical manner. Four possibitities are investigated: axiomatic approach to causal theory of space-time, the smooth toposes as a models of Theory of Relativity, Synthetic Theory of Relativity, and space-time as Grothendieck topos.

17 citations

Book ChapterDOI
01 Jan 2005

17 citations

Posted Content
TL;DR: In this article, the conservation condition is best understood as a consequence of the differential equations governing the evolution of matter in general relativity and many other theories, and the relationship between that geometry and the dynamical properties of matter is discussed.
Abstract: As Harvey Brown emphasizes in his book Physical Relativity, inertial motion in general relativity is best understood as a theorem, and not a postulate. Here I discuss the status of the "conservation condition", which states that the energy-momentum tensor associated with non-interacting matter is covariantly divergence-free, in connection with such theorems. I argue that the conservation condition is best understood as a consequence of the differential equations governing the evolution of matter in general relativity and many other theories. I conclude by discussing what it means to posit a certain spacetime geometry and the relationship between that geometry and the dynamical properties of matter.

17 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that no static nonsingular solution of the general relativity equations exists for the gravitational field of an uniformly planar matter distribution under very general assumptions.
Abstract: It is shown that, under very general assumptions, no static nonsingular solution of the general relativity equations exists for the gravitational field of an uniformly planar matter distribution.

17 citations


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