quartonews.it » Math and Science » Stability by Linearization of Einstein's Field Equation (Progress in Mathematical Physics)

Author: | Lluís Bruna,Joan Girbau |

Subcategory: | Mathematics |

Language: | English |

Publisher: | Birkhäuser; 2010 edition (April 8, 2010) |

Pages: | 208 pages |

Category: | Math and Science |

Rating: | 4.4 |

Other formats: | lrf txt doc azw |

Approximation of Einstein’s Equation by the Wave Equation. Pages 49-62 Bibliographic Information. Stability by Linearization of Einstein's Field Equation.

Approximation of Einstein’s Equation by the Wave Equation. General Results on Stability by Linearization when the Submanifold M of V is Compact. Bibliographic Information. Progress in Mathematical Physics.

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Cauchy problem for Einstein’s equation EFE Einstein's equation Gravity Pseudo-Riemannian manifolds Relativity Robertson-Walker models Sobolev spaces Special relativity Stability by linearization general relativity. Authors and affiliations. 1. epartament de MatemàtiquesUniversitat Autònoma de ain.

Электронная книга "Stability by Linearization of Einstein's Field . The book’s focus is on both the equations and their methods of solution.

Электронная книга "Stability by Linearization of Einstein's Field Equation", Lluís Bruna, Joan Girbau. Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced undergraduate- or graduate-level text considers only those problems leading to partial differential equations.

by Lluís Bruna (Author), Joan Girbau (Author).

Buchreihe: Progress in Mathematical Physics. Autoren: Joan Girbau, Lluís Bruna. Verlag: Birkhäuser Basel

Buchreihe: Progress in Mathematical Physics. Verlag: Birkhäuser Basel. Print ISBN: 978-3-0346-0303-4. This chapter will deal with a study of stability by linearization of Einstein’s equation when the initial metric and the initial stress-energy tensor are those from a Robertson-Walker cosmological model.

This book details the mathematical framework in which linearization stability of Einstein equation with matter makes sense. It then examines conditions for this type of stability when a Robertson-Walker model for the universe is considered. The concept of linearization stability arises when one compares the solutions to a linearized equation with solutions to the corresponding true equation. This requires a new definition of linearization stability adapted to Einstein's equation. However, this new definition cannot be applied directly to Einstein's equation because energy conditions.

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In general theory of relativity the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of space-time with the distribution of matter within it. The equations were first published by Einstein in 1915 in the form of a tensor equation which related the local spacetime curvature (expressed by the Einstein tensor) with the local energy and momentum within that spacetime (expressed by the stress–energy tensor).

Authors: Bruna, Lluis. 24 cm. ISBN: 3034603037 Subject(s): Quantum field theory %Mathematics. Mathematical physics. joint author Series: Progress in mathematical physics ;. v. 58. Published by : Birkhauser, (Basel :) Physical details: xv, 208 p. : ill. ; 24 cm. Tags from this library

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

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