General Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the mathematical and numerical study of these motions is still in its infancy. It is believed that General Relativity models our cosmos, with a manifold of dimensions possibly greater than four and debatable topology opening a vast field of investigation for mathematicians and physicists alike. Remarkable conjectures have been proposed, many results have been obtained but many fundamental questions remain open. In this monograph, aimed at researchers in mathematics and physics, the author overviews the basic ideas in General Relativity, introduces the necessary mathematics and discusses some of the key open questions in the field.
General Relativity and the Einstein Equations
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"Yvonne Choquet-Bruhat's General Relativity and the Einstein Equations stands out from the crowd and is a remarkable resource. Choquet-Bruhat and her guests explain many difficult points in the theory with a rigor and clarity not found anywhere else. But the book is also a refreshing exposition of what is not known: The reader will come away feeling that general relativity has many exciting aspects to it just waiting to be discovered."--Physics Today
About the Author
Yvonne Choquet-Bruhat is a Membre de l'Academie des Sciences in Paris.
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9 of 11 people found the following review helpful:
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Best Review of Constraints in General Relativity,
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This review is from: General Relativity and the Einstein Equations (Oxford Mathematics (Hardcover Unnumbered)) (Hardcover)
Okay, this book has positive and negative aspects to it.
First the negative aspects. There are typos, which should be expected for such a huge book's first edition. Some are severe, others are not (e.g. when showing a rank-2 tensor is symmetric, it writes $X_{ab}=X_{ab}$ instead of $X_{ab}=X_{ba}$). These are the only negatives that come to mind. The positives are that this is probably the most (if not *the*) authoritative reference on constraints in general relativity. It covers York's conformally formulated constraints, and Moncrief's contributions as well. This is done in a scholarly manner, so one can refer to the original sources, and in a self-contained cohesive manner (so you don't have to refer to the original sources). It is really quite beautifully written. It may be a bit intimidating for the uninitiated working with constraints. I cannot help but apologize to the neophytes, I know no good introduction to the canonical formulation of gravity (except perhaps Poisson's book "The Relativist's Toolkit"). I cannot really deem this either a good or bad introduction, I was using the book as a reference. There are exercises, however, so if the reader performs all the exercises...she will be far more astute when it comes to the computations and theory behind esoteric topics in general relativity. But wait, there's more! This book covers black holes (in a rather mathematical way, so all of your favorite singularity theorems are here presented with proofs in a cohesive and beautifully well written manner). My two cents is to refer to this book when working on canonical formulations of gravity; I am currently in a reading group on black hole thermodynamics, and this book is my first recommendation to other students in the group.
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We give in this chapter a survey of the basic definitions of Riemannian and Lorentzian differential geometry that we will use in this book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
hyperbolic differential equations, compact causal domain, quasidiagonal system, contravariant associate, physically reasonable sources, weak cosmic censorship conjecture, spacelike isometry group, spatial isometry, strong cosmic censorship conjecture, densitized lapse, stress energy tensor, causal subset, wave gauge, wave map equation, inextendible curve, conformal killing fields, global hyperbolicity, given traceless, mean extrinsic curvature, inextendible causal curve, harmonicity conditions, stationary spacetimes, global existence proofs, quasilinear wave equations, relativistic kinetic theory Key Phrases - Capitalized Phrases (CAPs): (learn more)
General Relativity, Special Relativity, Local Cauchy, Pures Appl, Big Bang, Fundamental Regularity Hypothesis, Proof One, Conformally Formulated, Proof Straightforward, Cambridge University Press, Princeton University Press, New York, Pure Appl, Proof Suppose, Lecture Notes, Acta Mathematica, Yang Mills, Constraints Theorem, University of Chicago Press, World Scientific, Euclidean Einsteinian, Current Research, The Reissner-Nordström, Proof Let, Batelle Rencontres Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
We give in this chapter a survey of the basic definitions of Riemannian and Lorentzian differential geometry that we will use in this book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
hyperbolic differential equations, compact causal domain, quasidiagonal system, contravariant associate, physically reasonable sources, weak cosmic censorship conjecture, spacelike isometry group, spatial isometry, strong cosmic censorship conjecture, densitized lapse, stress energy tensor, causal subset, wave gauge, wave map equation, inextendible curve, conformal killing fields, global hyperbolicity, given traceless, mean extrinsic curvature, inextendible causal curve, harmonicity conditions, stationary spacetimes, global existence proofs, quasilinear wave equations, relativistic kinetic theory Key Phrases - Capitalized Phrases (CAPs): (learn more)
General Relativity, Special Relativity, Local Cauchy, Pures Appl, Big Bang, Fundamental Regularity Hypothesis, Proof One, Conformally Formulated, Proof Straightforward, Cambridge University Press, Princeton University Press, New York, Pure Appl, Proof Suppose, Lecture Notes, Acta Mathematica, Yang Mills, Constraints Theorem, University of Chicago Press, World Scientific, Euclidean Einsteinian, Current Research, The Reissner-Nordström, Proof Let, Batelle Rencontres Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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