The book presents state-of-the-art results on the analysis of the Einstein equations and the large scale structure of their solutions. It combines in a unique way introductory chapters and surveys of various aspects of the analysis of the Einstein equations in the large. It discusses applications of the Einstein equations in geometrical studies and the physical interpretation of their solutions. Open problems concerning analytical and numerical aspects of the Einstein equations are pointed out. Background material on techniques in PDE theory, differential geometry, and causal theory is provided.
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Yvonne Choquet-Bruhat's epic work of over 50 years ago shows that if a set of smooth initial data which satisfies the Einstein constraint equations is given, then we can always find a spacetime solution of the Einstein equations which contains an embedded hypersurface whose metric and second fundamental form agree with the chosen data. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
null mean curvature, mill infinity, reduced field equations, conformal field equations, conformal geodesics, vacuum constraint equations, inverse mean curvature flow, constant mean curvature foliations, future geodesically, thin sandwich approach, wave map equation, lapse equation, sharp growth estimates, mean curvature solutions, global existence problem, conformal flow, hyperboloidal data, achronal boundaries, static vacuum solutions, sandwich conjecture, smooth asymptotic structure, chronology horizon, gauge vector field, static field equations, positive mass theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Bel Robinson, Riemannian Penrose, New York, Classical Quantum Gravity, Vincent Moncrief, Lars Andersson, James Isenberg, Cambridge University Press, Yvonne Choquet-Bruhat, Helmut Friedrich, Henri Poincaré, Marsha Weaver, Princeton University Press, Symmetric Einsteinian, Pure Appl, Springer Verlag, David Garfinkle, Differential Geom, Global Anal, Marcel Dekker, University of Chicago Press, Valiente Kroon, Academic Press, Annals of Math, Australian National University New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Yvonne Choquet-Bruhat's epic work of over 50 years ago shows that if a set of smooth initial data which satisfies the Einstein constraint equations is given, then we can always find a spacetime solution of the Einstein equations which contains an embedded hypersurface whose metric and second fundamental form agree with the chosen data. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
null mean curvature, mill infinity, reduced field equations, conformal field equations, conformal geodesics, vacuum constraint equations, inverse mean curvature flow, constant mean curvature foliations, future geodesically, thin sandwich approach, wave map equation, lapse equation, sharp growth estimates, mean curvature solutions, global existence problem, conformal flow, hyperboloidal data, achronal boundaries, static vacuum solutions, sandwich conjecture, smooth asymptotic structure, chronology horizon, gauge vector field, static field equations, positive mass theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Bel Robinson, Riemannian Penrose, New York, Classical Quantum Gravity, Vincent Moncrief, Lars Andersson, James Isenberg, Cambridge University Press, Yvonne Choquet-Bruhat, Helmut Friedrich, Henri Poincaré, Marsha Weaver, Princeton University Press, Symmetric Einsteinian, Pure Appl, Springer Verlag, David Garfinkle, Differential Geom, Global Anal, Marcel Dekker, University of Chicago Press, Valiente Kroon, Academic Press, Annals of Math, Australian National University New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 30
books:
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- General Relativity by Robert M. Wald on page 38, page 115, and page 250
- The Evolution Problem in General Relativity by Sergiu Klainerman in Front Matter, page 202, and Back Matter
- The Large Scale Structure of Space-Time (Cambridge Monographs on Mathematical Physics) by Stephen W. Hawking in Front Matter, and page 345
- Partial Differential Equations (Applied Mathematical Sciences) (v. 1) by Fritz John on page 37, and page 112
- Mathematical Physics (Chicago Lectures in Physics) by Robert Geroch on page 36, and page 115
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