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Ultraspinning instability: the missing link

Oscar J. C. Dias, Ricardo Monteiro, Jorge E. Santos

TL;DR

The paper investigates the stability of Myers-Perry black holes in seven dimensions with two unequal spins, focusing on axisymmetric perturbations that preserve the background isometries. By solving a generalized Lichnerowicz eigenvalue problem in TT gauge, the authors map out zero-modes and identify onset lines for ultraspinning instabilities, demonstrating a continuous connection between the singly-spinning and cohomogeneity-1 sectors. They show that the first ultraspinning onset occurs before extremality and that all near-extremal solutions within this sub-family are unstable, raising questions about the existence of stable extremal MP black holes in d>5. The work provides a concrete link between different instability sectors, supports the ultraspinning conjecture, and has implications for the phase structure and possible bifurcations to new black hole families 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.

Ultraspinning instability: the missing link

TL;DR

The paper investigates the stability of Myers-Perry black holes in seven dimensions with two unequal spins, focusing on axisymmetric perturbations that preserve the background isometries. By solving a generalized Lichnerowicz eigenvalue problem in TT gauge, the authors map out zero-modes and identify onset lines for ultraspinning instabilities, demonstrating a continuous connection between the singly-spinning and cohomogeneity-1 sectors. They show that the first ultraspinning onset occurs before extremality and that all near-extremal solutions within this sub-family are unstable, raising questions about the existence of stable extremal MP black holes in d>5. The work provides a concrete link between different instability sectors, supports the ultraspinning conjecture, and has implications for the phase structure and possible bifurcations to new black hole families 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.

Paper Structure

This paper contains 10 sections, 32 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Myers-Perry black holes with two unequal spins
  3. Solution
  4. Thermodynamic zero-modes and the ultraspinning regime
  5. Ultraspinning perturbations of MP black holes
  6. Perturbations and eigenvalue problem
  7. Boundary conditions
  8. Strategy to find the unstable modes
  9. Results and discussion
  10. Boundary conditions at $v=|a|$ and $v=|b|$

Figures (1)

  • Figure 1: Phase diagram of MP solutions with two unequal spins in $d=7$. The axes are the rotation parameters $a$ and $b$, normalized to the horizon radius $r_+$. The colour code is the number of negative modes found numerically: red 1, blue 2, violet 3, green 4, brown 5, yellow 6. The blue line represents extremality, the black line between red and blue represents the ultraspinning surface, and the line between the blue and violet regions is the onset of the ultraspinning instability. The scattered white dots are numerical faults.