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It is shown how the extended conformal Einstein field equations and a gaugebased on the properties of conformal geodesics can be used to analyse thenon-linear stability of Einstein spaces with negative scalar curvature. Thisclass of spacetimes admits a smooth conformal extension with a spacelikeconformal boundary. Central to the analysis is the use of conformal Gaussiansystems to obtain a hyperbolic reduction of the conformal Einstein fieldequations for which standard Cauchy stability results for symmetric hyperbolicsystems can be employed. The use of conformal methods allows to rephrase thequestion of global existence of solutions to the Einstein field equations intoconsiderations of finite existence time for the conformal evolution system.

A conformal approach to the stability of Einstein spaces with spatial sections of negative scalar curvature