Description |
1 online resource (xv, 208 pages) : illustrations |
Series |
Progress in physics ; v. 58 |
|
Progress in mathematical physics ; v. 58.
|
Contents |
I. Pseudo-Riemannian manifolds -- II. Introduction to relativity -- III. Approximation of Einstein's equation by the wave equation -- IV. Cauchy problem for Einstein's equation with matter -- V. Stability by linearization of Einstein's equation, general concepts -- VI. General results on stability by linearization when the submanifold M of V is compact -- VII. Stability by linearization of Einstein's equation at Minkowski's initial metric -- VIII. Stability by linearization of Einstein's equation in Robertson-Walker cosmological models |
Summary |
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 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 |
Bibliography |
Includes bibliographical references and index |
Notes |
Print version record |
Subject |
Quantum field theory -- Mathematics
|
|
Mathematical physics.
|
|
Teoría cuántica de campos -- Matemáticas
|
|
Física matemática
|
|
Mathematical physics
|
|
Quantum field theory -- Mathematics
|
|
Einstein-Feldgleichungen
|
Form |
Electronic book
|
Author |
Bruna, Lluís.
|
ISBN |
9783034603041 |
|
3034603045 |
|