Perturbations of the Asymptotic Region of the Schwarzschild-de Sitter Spacetime

作者：Gasperin Edgar^*; Kroon Juan A Valiente

来源：Annales Henri Poincare, 2017, 18(5): 1519-1591.

DOI：10.1007/s00023-016-0544-z

The conformal structure of the Schwarzschild-de Sitter space-time is analysed using the extended conformal Einstein field equations. To this end, initial data for an asymptotic initial value problem for the Schwarzschild-de Sitter spacetime are obtained. This initial data allow to understand the singular behaviour of the conformal structure at the asymptotic points where the horizons of the Schwarzschild-de Sitter spacetime meet the conformal boundary. Using the insights gained from the analysis of the Schwarzschild-de Sitter spacetime in a conformal Gaussian gauge, we consider nonlinear perturbations close to the Schwarzschild-de Sitter spacetime in the asymptotic region. We show that small enough perturbations of asymptotic initial data for the Schwarzschild-de Sitter spacetime give rise to a solution to the Einstein field equations which exists to the future and has an asymptotic structure similar to that of the Schwarzschild-de Sitter spacetime.

• 出版日期2017-5