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.
Marc Mars (Salamanca): On staticity of bifurcate Killing horizons
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- Mars_13_March2024.pdf 141 KB
