Conformal properties of the Schwarzschild-de Sitter spacetime

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Written by Edgar Gasperin-Garcia

This talk is based on a work in collaboration with Juan Valiente Kroon.

Conformal methods constitute a powerful tool for the global analysis of spacetimes, e.g., in the proof of the global non-linear stability of de Sitter and the semiglobal non-linear stability of the Minkowski spacetime. In this talk we will briefly discuss the conformal Einstein field equations and conformal Gaussian systems. In addition, we will discuss how to use this formalism to pose an asymptotic initial value problem (the initial hypersurface is the conformal boundary) and analyse non-linear perturbations close to the Schwarzschild-de Sitter spacetime in the asymptotic region. In particular, it will be shown 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.