Progress in Mathematical Physics

Stability by Linearization of Einstein's Field Equation

Authors: Bruna, Lluís, Girbau, Joan

  • Contains classical results on stability of great beauty
  • Presents the objects needed to prove the theorems and the Cauchy problem for Einstein's equation in a self-contained way
  • Provides introductory chapters on pseudo-Riemannian manifolds and relativity (both special and general) addressed to readers having no background in these topics and a new definition of stability of Einstein's equation adapted to the case of matter and gives results concerning stability in Robertson-Walker models
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Hardcover $129.00
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About this book

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

Reviews

From the reviews:

“The authors of the book under review have contributed to this subject over the last ten years by studying the linearization stability for Einstein’s equations with source terms and in cosmological solutions. Here they present the results in a systematic fashion accessible to a reader with some background in differential geometry and partial differential equations.” (Hans-Peter Künzle, Mathematical Reviews, Issue 2011 h)

Table of contents (8 chapters)

  • Pseudo-Riemannian Manifolds

    Girbau, Joan (et al.)

    Pages 1-17

  • Introduction to Relativity

    Girbau, Joan (et al.)

    Pages 19-48

  • Approximation of Einstein’s Equation by the Wave Equation

    Girbau, Joan (et al.)

    Pages 49-62

  • Cauchy Problem for Einstein’s Equation with Matter

    Girbau, Joan (et al.)

    Pages 63-108

  • Stability by Linearization of Einstein’s Equation, General Concepts

    Girbau, Joan (et al.)

    Pages 109-128

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-0346-0304-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-0346-0303-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Stability by Linearization of Einstein's Field Equation
Authors
Series Title
Progress in Mathematical Physics
Series Volume
58
Copyright
2010
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-0346-0304-1
DOI
10.1007/978-3-0346-0304-1
Hardcover ISBN
978-3-0346-0303-4
Series ISSN
1544-9998
Edition Number
1
Number of Pages
XV, 208
Topics