Dynamic and Thermodynamic Stability of Black Holes and Black Branes
APA
Wald, R. (2013). Dynamic and Thermodynamic Stability of Black Holes and Black Branes. Perimeter Institute. https://pirsa.org/13060014
MLA
Wald, Robert. Dynamic and Thermodynamic Stability of Black Holes and Black Branes. Perimeter Institute, Jun. 13, 2013, https://pirsa.org/13060014
BibTex
@misc{ pirsa_PIRSA:13060014, doi = {10.48660/13060014}, url = {https://pirsa.org/13060014}, author = {Wald, Robert}, keywords = {Strong Gravity}, language = {en}, title = {Dynamic and Thermodynamic Stability of Black Holes and Black Branes}, publisher = {Perimeter Institute}, year = {2013}, month = {jun}, note = {PIRSA:13060014 see, \url{https://pirsa.org}} }
University of Chicago
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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 $\mathcal E = \delta^2 M - \sum_i \Omega_i \delta^2 J_i - (\kappa/8\pi) \delta^2 A$, 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.
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.