Einstein’s Field Equations and Their Physical Implications
Einstein’s Field Equations and Their Physical Implications

Author: Bernd G. Schmidt

Publisher: Springer

Published: 2008-01-11

Total Pages: 443

ISBN-13: 3540465804

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This book serves two purposes. The authors present important aspects of modern research on the mathematical structure of Einstein's field equations and they show how to extract their physical content from them by mathematically exact methods. The essays are devoted to exact solutions and to the Cauchy problem of the field equations as well as to post-Newtonian approximations that have direct physical implications. Further topics concern quantum gravity and optics in gravitational fields. The book addresses researchers in relativity and differential geometry but can also be used as additional reading material for graduate students.

Exact Solutions of Einstein's Field Equations
Exact Solutions of Einstein's Field Equations

Author: Hans Stephani

Publisher: Cambridge University Press

Published: 2009-09-24

Total Pages: 732

ISBN-13: 9780521467025

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A completely revised and updated edition of this classic text, covering important new methods and many recently discovered solutions. This edition contains new chapters on generation methods and their application, classification of metrics by invariants, and treatments of homothetic motions and methods from dynamical systems theory. It also includes colliding waves, inhomogeneous cosmological solutions, and spacetimes containing special subspaces.

The Einstein Equations and the Large Scale Behavior of Gravitational Fields
The Einstein Equations and the Large Scale Behavior of Gravitational Fields

Author: Piotr T. Chruściel

Publisher: Springer Science & Business Media

Published: 2004

Total Pages: 500

ISBN-13: 9783764371302

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Accompanying DVD-ROM contains the electronic proceedings of the summer school on mathematical general relativity and global properties of solutions of Einstein's equations held at Cargèse, Corsica, France, July 20-Aug. 10, 2002.

Stability by Linearization of Einstein's Field Equation
Stability by Linearization of Einstein's Field Equation

Author: Lluís Bruna

Publisher: Springer Science & Business Media

Published: 2013-11-25

Total Pages: 220

ISBN-13: 3034603045

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V ? V ?K? , 3 2 2 R ? /?x K i i g V T G g ?T , ? G g g 4 ? R ? ? G ? T g g ? h h ? 2 2 2 2 ? ? ? ? ? ? ? h ?S , ?? ?? 2 2 2 2 2 c ?t ?x ?x ?x 1 2 3 S T S T? T?. ? ̃ T S 2 2 2 2 ? ? ? ? ? ? ? h . ?? 2 2 2 2 2 c ?t ?x ?x ?x 1 2 3 g h h ?? g T T g vacuum M n R n R Acknowledgements n R Chapter I Pseudo-Riemannian Manifolds I.1 Connections M C n X M C M F M C X M F M connection covariant derivative M ? X M ×X M ?? X M X,Y ?? Y X ? Y ? Y ? Y X +X X X 1 2 1 2 ? Y Y ? Y ? Y X 1 2 X 1 X 2 ? Y f? Y f?F M fX X ? fY X f Y f? Y f?F M X X ? torsion ? Y?? X X,Y X,Y?X M . X Y localization principle Theorem I.1. Let X, Y, X , Y be C vector ?elds on M.Let U be an open set

The Einstein Equations and the Large Scale Behavior of Gravitational Fields
The Einstein Equations and the Large Scale Behavior of Gravitational Fields

Author: Piotr T. Chrusciel

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 487

ISBN-13: 3034879539

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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.

General Relativity
General Relativity

Author: Michael J W Hall

Publisher: Morgan & Claypool Publishers

Published: 2018-03-23

Total Pages: 159

ISBN-13: 1681748843

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This book is based on a set of 18 class-tested lectures delivered to fourth-year physics undergraduates at Griffith University in Brisbane, and the book presents new discoveries by the Nobel-prize winning LIGO collaboration. The author begins with a review of special relativity and tensors and then develops the basic elements of general relativity (a beautiful theory that unifies special relativity and gravitation via geometry) with applications to the gravitational deflection of light, global positioning systems, black holes, gravitational waves, and cosmology. The book provides readers with a solid understanding of the underlying physical concepts; an ability to appreciate and in many cases derive important applications of the theory; and a solid grounding for those wishing to pursue their studies further. General Relativity: An Introduction to Black Holes, Gravitational Waves, and Cosmology also connects general relativity with broader topics. There is no doubt that general relativity is an active and exciting field of physics, and this book successfully transmits that excitement to readers.

The Geometry of Spacetime
The Geometry of Spacetime

Author: James J. Callahan

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 474

ISBN-13: 1475767366

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Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory.

Gravitation: Following The Prague Inspiration: A Volume In Celebration Of The 60th Birthday Of Jiri Bicak
Gravitation: Following The Prague Inspiration: A Volume In Celebration Of The 60th Birthday Of Jiri Bicak

Author: J Podolsky

Publisher: World Scientific

Published: 2002-08-13

Total Pages: 346

ISBN-13: 9814487945

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This volume is dedicated to Jirí Bičák on the occasion of his 60th birthday. The authors are his former students who currently work in the fields of general relativity, astrophysics, theoretical physics and cosmology. Unlike in traditional Festschrifts with many short contributions, they present several comprehensive surveys and elaborate original works. The subjects range from the motion of stars in galactic nuclei to quantum mechanics on a boundary, and include current topics such as cosmological perturbations, effects of a repulsive cosmological constant, discs around black holes and gravitational waves. An unconventional introductory essay revives Prague's inspirations as personified by Tycho Brahe, Johannes Kepler, Christian Doppler, Ernst Mach, Albert Einstein and others.

General Relativity and the Einstein Equations
General Relativity and the Einstein Equations

Author: Yvonne Choquet-Bruhat

Publisher: Oxford University Press

Published: 2009

Total Pages: 812

ISBN-13: 0199230722

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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.

Beyond Partial Differential Equations
Beyond Partial Differential Equations

Author: Horst Reinhard Beyer

Publisher: Springer

Published: 2007-04-10

Total Pages: 291

ISBN-13: 3540711295

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This book introduces the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis, with only some examples requiring more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Emphasis is placed on equations of the hyperbolic type which are less often treated in the literature.