## Stability by Linearization of Einstein's Field EquationThe 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 tie together deformations of the metric and of the stress-energy tensor. Therefore, a background is necessary where the variables representing the geometry and the energy-matter are independent. This representation is given by a well-posed Cauchy problem for Einstein's field equation. This book establishes a precise mathematical framework in which linearization stability of Einstein's equation with matter makes sense. Using this framework, conditions for this type of stability in Robertson-Walker models of the universe are discussed. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

PseudoRiemannian Manifolds | 1 |

Introduction to Relativity | 19 |

Approximation of Einsteins Equation | 49 |

Copyright | |

6 other sections not shown

### Other editions - View all

Stability by Linearization of Einstein's Field Equation Lluís Bruna,Joan Girbau Limited preview - 2013 |

Stability by Linearization of Einstein's Field Equation Lluís Bruna,Joan Girbau No preview available - 2011 |

### Common terms and phrases

already appear apply associated Assume Banach spaces basis belonging bundle calculate called Cauchy data Chapter chart classical coefficients compact components concept connection consider constant containing continuous coordinates corresponding covariant curvature defined definition denote depend derivatives differentiable dimension Einstein's equation element equality exists expression fact fixed force formula function given gives hyperbolic hypersurface identity implies inertial system initial metric inner product integral introduced isomorphism Laplacian Lemma linearization Lorentzian metric manifold matrix matter means metric ğ neighborhood observer obtain open set operator origin pair particle positive proof Proposition prove Recall reference region relativity respect result Riemannian satisfying side Sobolev spaces solution special relativity stability by linearization straight line stress-energy tensor Suppose symmetric tangent Theorem transformation vacuum values vanishes vector field write written zero