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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 paper, the uniqueness of the static solutions of Einstein's equation that represent isolated uniform-density perfect-fluid stellar models is demonstrated: any static asymptotically flat space-time containing only a uniform density perfect fluid confined to a spatially compact world tube is necessarily spherically symmetric.
Abstract: In this paper the uniqueness of the static solutions of Einstein’s equation that represent isolated uniform‐density perfect‐fluid stellar models is demonstrated: any static asymptotically flat space‐time containing only a uniform‐density perfect fluid confined to a spatially compact world tube is necessarily spherically symmetric. This result generalizes to relativistic uniform‐density models the well known Newtonian theorem of Carleman and Lichtenstein.
32 citations
TL;DR: In this article, the Riemann-Einstein tensor of general relativity as well as chiral and super-symmetry are utilized to develop various extended versions of the standard model of high energy physics.
Abstract: The Riemann–Einstein tensor of general relativity as well as chiral and super-symmetry are utilized to develop various extended versions of the standard model of high energy physics. Based on these models, it is possible to predict that few new elementary particles conjectured to be the Higgs are likely to be found experimentally at an energy scale which is just above that of the electroweak. Connections to the massless states of different super-string theories as well as super-gravity are also discussed.
32 citations
TL;DR: In this article, a conformal approach to the numerical simulation of radiating isolated systems in general relativity is discussed. But the conformal method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled variables, the so-called conformal field equations developed by Friedrich.
Abstract: I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled variables, the so-called “conformal field equations” developed by Friedrich These equations allow to include “infinity” on a finite grid, solving regular equations, whose solutions give rise to solutions of the Einstein equations of (vacuum) general relativity The conformal approach promises certain advantages, in particular with respect to the treatment of radiation extraction and boundary conditions I will discuss the essential features of the analytical approach to the problem, previous work on the problem— in particular a code for simulations in 3+1 dimensions, some new results, open problems and strategies for future work
32 citations
TL;DR: In this paper, it was shown that any extendible spacetime U has a maximal extension containing no closed causal curves outside the chronological past of U. The authors interpreted this fact as the impossibility of time machines.
Abstract: Irrespective of local conditions imposed on the metric, any extendible spacetime U has a maximal extension containing no closed causal curves outside the chronological past of U. We prove this fact and interpret it as impossibility (in classical general relativity) of the time machines, insofar as the latter are defined to be causality-violating regions created by human beings (as opposed to those appearing spontaneously).
32 citations
TL;DR: In this paper, it was shown that a space-time admitting a nonsingular 2-form satisfying the source-free Maxwell equations and a Lorentzian involution under which the 2form and the exterior derivative of related 2-forms are skew invariant while the trace-free Ricci tensor and the covariant derivative of the involution itself are invariant possesses locally an invertible 2-parameter Abelian isometry group.
Abstract: It is shown that a space-time admitting a nonsingular 2-form satisfying the source-free Maxwell equations and a Lorentzian involution under which the 2-form and the exterior derivative of a related 2-form are skew invariant while the trace-free Ricci tensor and the covariant derivative of the involution itself are invariant possesses locally an invertible 2-parameter Abelian isometry group with nonsingular orbits
32 citations