# 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}
}
• Published 2 January 2012
• Physics
• Communications in Mathematical Physics
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…
136 Citations
Dynamic and Thermodynamic Stability of Black Holes and Black Branes
I describe recent work with Stefan Hollands that establishes a new criterion for the dynamical stability of black holes in $$D \ge 4$$ spacetime dimensions in general relativity with respect to
Black Hole Instabilities and Exponential Growth
• Mathematics
• 2015
Recently, a general analysis has been given of the stability with respect to axisymmetric perturbations of stationary-axisymmetric black holes and black branes in vacuum general relativity in
Instabilities of Extremal Rotating Black Holes in Higher Dimensions
• Mathematics
• 2014
Recently, Durkee and Reall have conjectured a criterion for linear instability of rotating, extremal, asymptotically Minkowskian black holes in $${d\ge 4}$$d≥4 dimensions, such as the Myers–Perry
Boundedness and Decay for the Teukolsky Equation on Kerr Spacetimes I: The Case $$|a|\ll M$$|a|≪M
• Mathematics
Annals of PDE
• 2019
Boundedness and polynomial decay statements for solutions of the spin Teukolsky equation on a Kerr exterior background are proved, providing the first step in proving the full linear stability of the Kerr metric to gravitational perturbations.
Entanglement entropy and subregion complexity in thermal perturbations around pure AdS spacetime
• Physics
Physical Review D
• 2019
We compute the holographic entanglement entropy and subregion complexity of spherical boundary subregions in the uncharged and charged AdS black hole backgrounds, with the \textbf{change} in these
Superradiant instabilities of asymptotically anti-de Sitter black holes
• Mathematics
• 2015
We study the linear stability of asymptotically anti-de Sitter black holes in general relativity in spacetime dimension $d\ge4$. Our approach is an adaptation of the general framework of Hollands and
On the interior geometry of a typical black hole microstate
• Physics
• 2018
A bstractWe argue that the region behind the horizon of a one-sided black hole can be probed by an analogue of the double-trace deformation protocol of Gao-Jafferis-Wall. This is achieved via a
News versus information
• Physics
Classical and Quantum Gravity
• 2019
We consider the relative entropy between the vacuum state and a coherent state in linearized quantum gravity around an asymptotically flat stationary black hole spacetime. Combining recent results by
Phase transition in anisotropic holographic superfluids with arbitrary $z$ and $\alpha$
• Physics
• 2016
Einstein-dilaton-$U(2)$ gauge field theory is considered in a spacetime characterised by $\alpha$ and $z$, which are the hyperscaling violation factor and the dynamical critical exponent
Lichnerowicz Modes and Black Hole Families in Ricci Quadratic Gravity
• Physics
• 2017
A new branch of black hole solutions occurs along with the standard Schwarzschild branch in $n$-dimensional extensions of general relativity including terms quadratic in the Ricci tensor. The

## References

SHOWING 1-10 OF 42 REFERENCES
Some properties of the Noether charge and a proposal for dynamical black hole entropy.
• Iyer, Wald
• Mathematics
Physical review. D, Particles and fields
• 1994
It is proved that the first law of black hole mechanics holds for arbitrary perturbations of a stationary black hole, and a local, geometrical prescription is proposed for the entropy, $S_{dyn}$, of a dynamical black hole.
Perturbations of near-horizon geometries and instabilities of Myers-Perry black holes
• Mathematics, Physics
• 2011
It is shown that the equations governing linearized gravitational (or electromagnetic) perturbations of the near-horizon geometry of any known extreme vacuum black hole (allowing for a cosmological
Energy extremality in the presence of a black hole
• Physics
• 1996
We derive the so-called first law of black hole mechanics for variations about stationary black hole solutions to the Einstein–Maxwell equations in the absence of sources. That is, we prove that δM =
A Generalization of Hawking’s Black Hole Topology Theorem to Higher Dimensions
• Mathematics
• 2005
Hawking’s theorem on the topology of black holes asserts that cross sections of the event horizon in 4-dimensional asymptotically flat stationary black hole spacetimes obeying the dominant energy
A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
• Mathematics
• 2006
A key result in the proof of black hole uniqueness in 4-dimensions is that a stationary black hole that is “rotating”—i.e., is such that the stationary Killing field is not everywhere normal to the
Symmetries of higher dimensional black holes
• Physics, Mathematics
• 2008
We prove that if a stationary, real analytic, asymptotically flat vacuum black hole spacetime of dimension n ≥ 4 contains a non-degenerate horizon with compact cross-sections that are transverse to
General variational principle for spherically symmetric perturbations in diffeomorphism covariant theories
• Mathematics, Physics
• 2007
We present a general method for the analysis of the stability of static, spherically symmetric solutions to spherically symmetric perturbations in an arbitrary diffeomorphism covariant Lagrangian
The evolution of unstable black holes in anti-de Sitter space
• Physics
• 2001
We examine the thermodynamic stability of large black holes in four-dimensional anti-de Sitter space, and we demonstrate numerically that black holes which lack local thermodynamic stability often
On mapping properties of the general relativistic constraints operator in weighted function spaces
• Mathematics
• 2003
Generalising an analysis of Corvino and Schoen, we study surjectivity properties of the constraint map in general relativity in a large class of weighted Sobolev spaces. As a corollary we prove
Asymptotic flatness and Bondi energy in higher dimensional gravity
• Mathematics
• 2005
We give a general geometric definition of asymptotic flatness at null infinity in d-dimensional general relativity (d even) within the framework of conformal infinity. Our definition is arrived at