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On stability of higher dimensional static black holes

Monday 5th September 2005 - 15:30 to 16:30
INI Seminar Room 1

I discuss the stability of black holes in static, electro-vacuum spacetimes of higher-dimension. I first provide a master equation for gravitational perturbations of black holes in higher dimensional static spacetimes, which corresponds to Regge-Wheeler-Zerilli equation in 4-dimensional case. Then i study the stability against linear gravitational perturbations by examining whether the spatial derivative part of the master equation has a positive self-adjoint extension. In this method, for example, higher-dimensional version of Schwarzschild black holes are shown to be stable. Using similar method, I also discuss some other static solutions e.g., generalised black holes, negative mass naked singularities, and the issue of possible boundary conditions at infinities or singularities.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons