Advances in Theoretical and Mathematical Physics

Volume 19 (2015)

Number 3

Horizon instability of extremal black holes

Pages: 507 – 530

DOI: https://dx.doi.org/10.4310/ATMP.2015.v19.n3.a1

Author

Stefanos Aretakis (Department of Mathematics, Princeton University, Princeton, New Jersey, U.S.A.; Institute for Advanced Study, Princeton, New Jersey, U.S.A.; and Department of Mathematics and Statistics, University of Reading, United Kingdom)

Abstract

We show that axisymmetric extremal horizons are unstable under scalar perturbations. Specifically, we show that translation invariant derivatives of generic solutions to the wave equation do not decay along such horizons as advanced time tends to infinity, and in fact, higher order derivatives blow up. This instability holds in particular for extremal Kerr–Newman and Majumdar–Papapetrou spacetimes and is in stark contrast with the subextremal case for which decay is known for all derivatives along the event horizon.

This result provides a entirely new aspect of the evolution of solutions to the wave equation along degenerate horizons and has a wealth of new applications.

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Published 19 October 2015