# Gravitational instability of an extreme Kerr black hole

@article{Lucietti2012GravitationalIO, title={Gravitational instability of an extreme Kerr black hole}, author={James Lucietti and Harvey S. Reall}, journal={Physical Review D}, year={2012}, volume={86}, pages={104030} }

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…

## 93 Citations

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

- Physics
- 2013

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

- Physics
- 2013

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

- Physics
- 2013

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

- Physics
- 2021

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?

- Physics
- 2013

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

- Physics
- 2018

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

- Mathematics
- 2014

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

- Physics
- 2018

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

- Physics
- 2019

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

- PhysicsAnnales Henri Poincaré
- 2014

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…

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