Stability of Black Holes and Black Branes

@article{Hollands2013StabilityOB,
  title={Stability of Black Holes and Black Branes},
  author={Stefan Hollands and Robert M. Wald},
  journal={Communications in Mathematical Physics},
  year={2013},
  volume={321},
  pages={629-680}
}
We establish a new criterion for the dynamical stability of black holes in D ≥ 4 spacetime dimensions in general relativity with respect to axisymmetric perturbations: Dynamical stability is equivalent to the positivity of the canonical energy, $${\mathcal{E}}$$, on a subspace, $${\mathcal{T}}$$, of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at infinity and satisfy certain gauge conditions at the horizon. This is shown by proving that—apart from… 
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