Abstract:
In this talk I will study the necessary and sufficient conditions that a spacetime admitting a bifurcate Killing horizon must satisfy to be static, i.e. such that the Killing of the horizon is hypersurface orthogonal. The result involves a bulk condition on the Ricci curvature, which is automatically satisfied for $\Lambda$-vacuum spacetimes, and a boundary condition on the data at the bifurcation surface.
The problem is solved in arbitrary dimension, and requires a different treatment in the region where the Killing is timelike (the exterior of the horizon) or spacelike (inside the horizon). This is joint work with Piotr T. Chrusciel.
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