Ultraspinning instability: the missing link

TL;DR

This paper investigates the linear stability of seven-dimensional Myers-Perry black holes with two equal angular momenta, revealing that instabilities occur before extremality and are connected to ultraspinning instabilities known in higher dimensions.

Contribution

It provides the first numerical analysis of the onset of ultraspinning instabilities in d=7 Myers-Perry black holes with two equal angular momenta, linking these to known instabilities in singly-spinning solutions.

Findings

Instabilities appear before extremality in d=7 Myers-Perry black holes.

The onset of instability connects solutions with one and multiple angular momenta.

Results suggest potential instability of all extremal Myers-Perry black holes in higher dimensions.

Abstract

We study linearized perturbations of Myers-Perry black holes in d=7, with two of the three angular momenta set to be equal, and show that instabilities always appear before extremality. Analogous results are expected for all higher odd d. We determine numerically the stationary perturbations that mark the onset of instability for the modes that preserve the isometries of the background. The onset is continuously connected between the previously studied sectors of solutions with a single angular momentum and solutions with all angular momenta equal. This shows that the near-extremality instabilities are of the same nature as the ultraspinning instability of d>5 singly-spinning solutions, for which the angular momentum is unbounded. Our results raise the question of whether there are any extremal Myers-Perry black holes which are stable in d>5.