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arXiv · 1506.00030

Perturbations of the asymptotic region of the Schwarzschild-de Sitter spacetime

Edgar Gasperin·Juan Antonio Valiente Kroon
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Abstract

The conformal structure of the Schwarzschild-de Sitter spacetime 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 is obtained. This initial data allows 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.

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Edgar Gasperin, Juan Antonio Valiente Kroon. 2015-05-29. Perturbations of the asymptotic region of the Schwarzschild-de Sitter spacetime. https://arxiv.org/abs/1506.00030

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