Dynamic and Thermodynamic Stability of Black Holes
Abstract
I describe recent work with with Stefan Hollands that establishes 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, E, on a subspace of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at infinity and satisfy certain gauge conditions at the horizon. We further show that E is related to the second order variations of mass, angular momentum, and horizon area by E = ^2M  ∑_{i}φ_{i}^2J_{i} (κ/8π) ^2A, thereby establishing a close connection between dynamical stability and thermodynamic stability. Thermodynamic instability of a family of black holes need not imply dynamical instability because the perturbations towards other members of the family will not, in general, have vanishing linearized ADM mass and/or angular momentum. However, we prove that all black branes corresponding to thermodynmically unstable black holes are dynamically unstable, as conjectured by Gubser and Mitra. We also prove that positivity of E is equivalent to the satisfaction of a ``local Penrose inequality,'' thus showing that satisfaction of this local Penrose inequality is necessary and sufficient for dynamical stability.
 Publication:

APS April Meeting Abstracts
 Pub Date:
 April 2013
 Bibcode:
 2013APS..APR.C5003W