Stability by Linearization of Einstein's Field Equation
by Llua-S Bruna (9783034603034)

Stability by Linearization of Einstein's Field Equation

Llua-S Bruna

Release Date: 19 February 2010
Format: Hardback
Pages: 208
Category: Mathematical Physics
Publisher: Birkhauser Basel
ISBN: 9783034603034
ISBN-10: 3034603037

The aim of this book is to establish the precise mathematical framework in which linearization stability of Einstein equation with matter makes sense, and once this is achieved, to find conditions for this type of stability when a Robertson-Walker model for the universe is considered. The concept of linearization stability arises when one wonders whether the solutions of a linearized equation do really approximate solutions of the corresponding true equation. This requires a new definition of linearization stability adapted to Einstein equation, a bit different from the classical one. However, this new definition can not be applied directly to the Einstein equation because energy conditions ties both deformations of the metric and of the stress-energy tensor. Therefore, one must look for a background where the variables representing the geometry and the energy-matter are independent. This representation is given by a well-posed Cauchy problem for the Einsteina (TM)s field equations.

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