Gravitational instability of an extreme Kerr black hole

  title={Gravitational instability of an extreme Kerr black hole},
  author={James Lucietti and Harvey S. Reall},
  journal={Physical Review D},
Aretakis has proved the existence of an instability of a massless scalar field at the horizon of an extreme Kerr or Reissner-Nordstrblack hole: for generic initial data, a transverse derivative of the scalar field at the horizon does not decay, and higher transverse derivatives blow up. We show that a similar instability occurs for linearized gravitational, and electromagnetic, perturbations of an extreme Kerr black hole. We show also that the massless scalar field instability occurs for… 

On the horizon instability of an extreme Reissner-Nordström black hole

A bstractAretakis has proved that a massless scalar field has an instability at the horizon of an extreme Reissner-Nordström black hole. We show that a similar instability occurs also for a massive

Horizon instability of massless scalar perturbations of an extreme Reissner-Nordström-AdS black hole

A bstractWe study the stability of extreme Reissner-Nordström-AdS black hole under massless scalar perturbations. We show that the perturbation on the horizon of the extreme Reissner-Nordström-AdS

Instability of higher dimensional extreme black holes

We study linearized gravitational perturbations of extreme black hole solutions of the vacuum Einstein equation in any number of dimensions. We find that the equations governing such perturbations

Scalar and gravitational hair for extreme Kerr black holes

For scalar perturbations of an extreme Reissner-Nordstr\"om black hole we show numerically that the Ori prefactor equals the Aretakis conserved charge. For a family of scalar or gravitational

What happens at the horizon(s) of an extreme black hole?

A massless scalar field exhibits an instability at the event horizon of an extreme black hole. We study numerically the nonlinear evolution of this instability for spherically symmetric perturbations

Critical exponents of extremal Kerr perturbations

We show that scalar, electromagnetic, and gravitational perturbations of extremal Kerr black holes are asymptotically self-similar under the near-horizon, late-time scaling symmetry of the background

On the linear stability of the extreme Kerr black hole under axially symmetric perturbations

We prove that for axially symmetric linear gravitational perturbations of the extreme Kerr black hole, there exists a positive definite and conserved energy. This provides a basic criteria for linear

Linearized stability of extreme black holes

Extreme black holes have been argued to be unstable, in the sense that under linearized gravitational perturbations of the extreme Kerr spacetime the Weyl scalar $\psi_4$ blows up along their event

Horizon instability of the extremal BTZ black hole

We study real-time propagation of a massive scalar field on the extremal BTZ black hole spacetime, focusing on the Aretakis instability of the event horizon. We obtain a simple time-domain expression

On Perturbations of Extreme Kerr–Newman Black Holes and their Evolution

Using black hole inequalities and the increase of the horizon’s areas, we show that there are arbitrarily small electro-vacuum perturbations of the standard initial data of the extreme



Perturbations of a rotating black hole. I. Fundamental equations for gravitational, electromagnetic, and neutrino-field perturbations

Decoupled, separable equations describing perturbations of a Kerr black hole are derived. These equations can be used to study black-hole processes involving scalar, electromagnetic, neutrino or

Unstable fields in Kerr spacetimes

We show that both the interior region of a Kerr black hole and the a2 > M2 Kerr naked singularity admit unstable solutions of the Teukolsky equation for any value of the spin weight. For every

Horizon Instability of Extremal Black Holes

We show that axisymmetric extremal horizons are unstable under linear scalar perturbations. Specifically, we show that translation invariant derivatives of generic solutions to the wave equation do


Separable wave equations with source terms are presented for electromagnetic and gravitational perturbations of an uncharged, rotating black hole. These equations describe the radiative field

Near-horizon symmetries of extremal black holes

Recent work has demonstrated an attractor mechanism for extremal rotating black holes subject to the assumption of a near-horizon SO(2, 1) symmetry. We prove the existence of this symmetry for any

The dangers of extremes

While extreme black hole spacetimes with smooth horizons are known at the level of mathematics, we argue that the horizons of physical extreme black holes are effectively singular. Test particles

Proof of the (local) angular momentum–mass inequality for axisymmetric black holes

  • S. Dain
  • Physics
    Physical review letters
  • 2006
The inequality square root J <or=m is proved for vacuum, asymptotically flat, maximal, and axisymmetric data close to extreme Kerr data and its relation to the standard picture of the gravitational collapse is discussed.

Charged shells in general relativity and their gravitational collapse

The boundary conditions for the gravitational and electromagnetic fields on charged shells are formulated. The shells are characterized in geometrical terms and the boundary conditions are manifestly