Stability by Linearization of Einstein’s Field Equation [electronic resource] / by Joan Girbau, Lluís Bruna.
By: Girbau, Joan [author.].
Contributor(s): Bruna, Lluís [author.] | SpringerLink (Online service).
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BookSeries: Progress in Mathematical Physics: 58Publisher: Basel : Birkhäuser Basel : Imprint: Birkhäuser, 2010Description: XV, 208p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783034603041.Subject(s): Mathematics | Differential equations, partial | Mathematics | Partial Differential Equations | Theoretical, Mathematical and Computational PhysicsDDC classification: 515.353 Online resources: Click here to access online
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Springer eBooksSummary: 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.
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.
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