Junior Analysis Seminar: Marica Minucci (Queen Mary)

The non-linear stability of the sub-extremal Schwarzschild-de Sitter spacetime in the stationary region near the conformal boundary can be analysed by means of a technique based on the extended conformal Einstein field equations and a conformal Gaussian gauge. The strategy relies on the observation that the cosmological stationary region of this exact solution can be covered by a non-intersecting congruence of conformal geodesics. Thus, the future domain dependence of suitable spacelike hypersurfaces in the Cosmological region of the spacetime can be expressed in terms of a conformal Gaussian gauge. A perturbative argument then allows to prove existence and stability results close to the conformal boundary and away from the asymptotic points where the cosmological horizon intersects the conformal boundary. In particular, small enough perturbations of
initial data for the sub-extremal Schwarzschild-de Sitter spacetime give rise to a solution to the Einstein field equations which is regular at the conformal boundary.