PIRSA:13060014  ( MP4 Medium Res , MP4 Low Res , MP3 , PDF ) Which Format?
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
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