Dynamic and Thermodynamic Stability of Black Holes and Black Branes Speaker(s): Robert Wald
Abstract: I describe recent work with with Stefan Hollands that establishes a new criterion for the dynamical stability of black holes in $D geq 4$ spacetime dimensions in general relativity with respect to axisymmetric perturbations: Dynamic stability is equivalent to the positivity of the canonical energy, $mathcal E$, 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 $mathcal E$ is related to the second order variations of mass, angular momentum, and horizon area by $mathcal E = delta^2 M  sum_i Omega_i delta^2 J_i  (kappa/8pi) delta^2 A$, thereby establishing a close connection between dynamic stability and thermodynamic stability.
Thermodynamic instability of a family of black holes need not imply dynamic 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 $mathcal E$ 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. Date: 13/06/2013  1:00 pm
Series: Strong Gravity
