Extensions of the Stability Theorem of the Minkowski Space in General Relativity (Ams/Ip Studies in Advanced Mathematics)

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9780821848234: Extensions of the Stability Theorem of the Minkowski Space in General Relativity (Ams/Ip Studies in Advanced Mathematics)

A famous result of Christodoulou and Klainerman is the global nonlinear stability of Minkowski spacetime. In this book, Bieri and Zipser provide two extensions to this result. In the first part, Bieri solves the Cauchy problem for the Einstein vacuum equations with more general, asymptotically flat initial data, and describes precisely the asymptotic behavior. In particular, she assumes less decay in the power of $r$ and one less derivative than in the Christodoulou-Klainerman result. She proves that in this case, too, the initial data, being globally close to the trivial data, yields a solution which is a complete spacetime, tending to the Minkowski spacetime at infinity along any geodesic. In contrast to the original situation, certain estimates in this proof are borderline in view of decay, indicating that the conditions in the main theorem on the decay at infinity on the initial data are sharp. In the second part, Zipser proves the existence of smooth, global solutions to the Einstein-Maxwell equations. A nontrivial solution of these equations is a curved spacetime with an electromagnetic field. To prove the existence of solutions to the Einstein-Maxwell equations, Zipser follows the argument and methodology introduced by Christodoulou and Klainerman. To generalize the original results, she needs to contend with the additional curvature terms that arise due to the presence of the electromagnetic field $F$; in her case the Ricci curvature of the spacetime is not identically zero but rather represented by a quadratic in the components of $F$. In particular the Ricci curvature is a constant multiple of the stress-energy tensor for $F$. Furthermore, the traceless part of the Riemann curvature tensor no longer satisfies the homogeneous Bianchi equations but rather inhomogeneous equations including components of the spacetime Ricci curvature. Therefore, the second part of this book focuses primarily on the derivation of estimates for the new terms that arise due to the presence of the electromagnetic field.

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Both parts are well written. ...the book should be of interest to anyone who is doing research in mathematical relativity. ---- Mathematical Reviews

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1.

Lydia Bieri, Nina Zipser
Editorial: American Mathematical Society, United States (2009)
ISBN 10: 0821848232 ISBN 13: 9780821848234
Nuevos Tapa dura Cantidad: 1
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The Book Depository US
(London, Reino Unido)
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Descripción American Mathematical Society, United States, 2009. Hardback. Estado de conservación: New. New ed.. Language: English . Brand New Book. This book consists of two independent works: Part I is Solutions of the Einstein Vacuum Equations , by Lydia Bieri. Part II is Solutions of the Einstein-Maxwell Equations , by Nina Zipser. A famous result of Christodoulou and Klainerman is the global nonlinear stability of Minkowski spacetime. In this book, Bieri and Zipser provide two extensions to this result. In the first part, Bieri solves the Cauchy problem for the Einstein vacuum equations with more general, asymptotically flat initial data, and describes precisely the asymptotic behavior. In particular, she assumes less decay in the power of $r$ and one less derivative than in the Christodoulou-Klainerman result. She proves that in this case, too, the initial data, being globally close to the trivial data, yields a solution which is a complete spacetime, tending to the Minkowski spacetime at infinity along any geodesic. In contrast to the original situation, certain estimates in this proof are borderline in view of decay, indicating that the conditions in the main theorem on the decay at infinity on the initial data are sharp. In the second part, Zipser proves the existence of smooth, global solutions to the Einstein-Maxwell equations. A nontrivial solution of these equations is a curved spacetime with an electromagnetic field. To prove the existence of solutions to the Einstein-Maxwell equations, Zipser follows the argument and methodology introduced by Christodoulou and Klainerman. To generalize the original results, she needs to contend with the additional curvature terms that arise due to the presence of the electromagnetic field $F$; in her case the Ricci curvature of the spacetime is not identically zero but rather represented by a quadratic in the components of $F$. In particular the Ricci curvature is a constant multiple of the stress-energy tensor for $F$. Furthermore, the traceless part of the Riemann curvature tensor no longer satisfies the homogeneous Bianchi equations but rather inhomogeneous equations including components of the spacetime Ricci curvature. Therefore, the second part of this book focuses primarily on the derivation of estimates for the new terms that arise due to the presence of the electromagnetic field. Nº de ref. de la librería AAN9780821848234

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2.

Lydia Bieri, Nina Zipser
Editorial: American Mathematical Society, United States (2009)
ISBN 10: 0821848232 ISBN 13: 9780821848234
Nuevos Tapa dura Cantidad: 1
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The Book Depository
(London, Reino Unido)
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Descripción American Mathematical Society, United States, 2009. Hardback. Estado de conservación: New. New ed.. Language: English . Brand New Book. This book consists of two independent works: Part I is Solutions of the Einstein Vacuum Equations , by Lydia Bieri. Part II is Solutions of the Einstein-Maxwell Equations , by Nina Zipser. A famous result of Christodoulou and Klainerman is the global nonlinear stability of Minkowski spacetime. In this book, Bieri and Zipser provide two extensions to this result. In the first part, Bieri solves the Cauchy problem for the Einstein vacuum equations with more general, asymptotically flat initial data, and describes precisely the asymptotic behavior. In particular, she assumes less decay in the power of $r$ and one less derivative than in the Christodoulou-Klainerman result. She proves that in this case, too, the initial data, being globally close to the trivial data, yields a solution which is a complete spacetime, tending to the Minkowski spacetime at infinity along any geodesic. In contrast to the original situation, certain estimates in this proof are borderline in view of decay, indicating that the conditions in the main theorem on the decay at infinity on the initial data are sharp. In the second part, Zipser proves the existence of smooth, global solutions to the Einstein-Maxwell equations. A nontrivial solution of these equations is a curved spacetime with an electromagnetic field. To prove the existence of solutions to the Einstein-Maxwell equations, Zipser follows the argument and methodology introduced by Christodoulou and Klainerman. To generalize the original results, she needs to contend with the additional curvature terms that arise due to the presence of the electromagnetic field $F$; in her case the Ricci curvature of the spacetime is not identically zero but rather represented by a quadratic in the components of $F$. In particular the Ricci curvature is a constant multiple of the stress-energy tensor for $F$. Furthermore, the traceless part of the Riemann curvature tensor no longer satisfies the homogeneous Bianchi equations but rather inhomogeneous equations including components of the spacetime Ricci curvature. Therefore, the second part of this book focuses primarily on the derivation of estimates for the new terms that arise due to the presence of the electromagnetic field. Nº de ref. de la librería AAN9780821848234

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Lydia Bieri and Nina Zipser
Editorial: American Mathematical Society (2009)
ISBN 10: 0821848232 ISBN 13: 9780821848234
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Descripción American Mathematical Society, 2009. Hardcover. Estado de conservación: New. Never used!. Nº de ref. de la librería P110821848232

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Bieri, Lydia/ Zipser, Nina
Editorial: American Mathematical Society (2009)
ISBN 10: 0821848232 ISBN 13: 9780821848234
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Revaluation Books
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Descripción American Mathematical Society, 2009. Hardcover. Estado de conservación: Brand New. 491 pages. 10.00x7.25x1.25 inches. In Stock. Nº de ref. de la librería __0821848232

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Lydia Bieri and Nina Zipser
Editorial: American Mathematical Society (2009)
ISBN 10: 0821848232 ISBN 13: 9780821848234
Nuevos Tapa dura Cantidad: 1
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Irish Booksellers
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Descripción American Mathematical Society, 2009. Hardcover. Estado de conservación: New. book. Nº de ref. de la librería M0821848232

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