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Stability of stationary-axisymmetric black holes in vacuum general relativity to axisymmetric electromagnetic perturbations
We consider arbitrary stationary and axisymmetric black holes in general relativity in dimensions (with ) that satisfy the vacuum Einstein equation and have a non-degenerate horizon. We prove that the canonical energy of axisymmetric electromagnetic perturbations is positive definite. This establishes that all vacuum black holes are stable to axisymmetric …