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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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01 Jan 1985TL;DR: Although general relativity is among the oldest and most studied nonlinear theories in physics, it has played only a modest role in the exciting soliton and chaos developments of recent years as discussed by the authors.
Abstract: Although general relativity is among the oldest and most studied of all nonlinear theories in physics, it has played only a modest role in the exciting soliton and chaos developments of recent years. There are three causes of this, I think: (i) The absence of any experimental data for strong gravity situations, which has protected relativists from having their noses rubbed in chaos; (ii) the extreme difficulty of solving Einstein’s equations, which has induced relativists to concentrate on situations of weak gravity or high symmetry where chaos is usually absent and soliton-like structures were recognized as such only recently; and (iii) inadequate communica tion between relativists and people working on solitons and chaos.
11 citations
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01 Jan 2007
TL;DR: In this paper, the double pulsar and the double Pulsar were used to test Einstein's gravity in space and the Gravity Probe B Relativity Mission (GPRB) in space.
Abstract: General Relativity today.- Beyond Einstein's Gravity.- The Double Pulsar.- Testing Einstein in Space: The Gravity Probe B Relativity Mission.- Instruments for Gravitational Wave Astronomy on Ground and in Space.
11 citations
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31 Mar 2005
TL;DR: In this paper, the fundamental concepts behind the field of numerical relativity are introduced, including the Cauchy problem, the 3+1 formalism, and finite differencing techniques for solving partial differential equations numerically.
Abstract: In this manuscript I give a brief introduction to the fundamental concepts behind the field of numerical relativity. I start by introducing the Cauchy problem and the 3+1 formalism. I discuss the constraint and evolution equations, gauge conditions and the problem of finding initial data. I also introduce some basic notions of finite differencing techniques for solving partial differential equations numerically. Finally I discuss some applications of numerical relativity to the study of black hole and neutron star spacetimes.
11 citations
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TL;DR: In this paper , an optimal transport formulation of the full Einstein equations of general relativity, linking the Ricci curvature of a space-time with the cosmological constant and the energy-momentum tensor, is given.
Abstract: The goal of the paper is to give an optimal transport formulation of the full Einstein equations of general relativity, linking the (Ricci) curvature of a space-time with the cosmological constant and the energy-momentum tensor. Such an optimal transport formulation is in terms of convexity/concavity properties of the Boltzmann–Shannon entropy along curves of probability measures extremizing suitable optimal transport costs. The result gives a new connection between general relativity and optimal transport; moreover, it gives a mathematical reinforcement of the strong link between general relativity and thermodynamics/information theory that emerged in the physics literature of the last years.
11 citations