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Bumpy black holes from spontaneous Lorentz violation

Sergei Dubovsky, Peter Tinyakov, Matias Zaldarriaga

TL;DR

The work addresses whether black holes remain hairless in theories with spontaneous Lorentz violation and a massive graviton. It shows that instantaneous interactions in the Higgs phase generate an infinite set of BH hairs, making the exterior geometry sensitive to the interior and undermining the universality of the Kerr solution. The hair amplitude scales with the graviton mass parameter $m_g$, so constraints on $m_g$ from binary pulsars strongly suppress observable bumps for most SMBHs, while the most massive systems with $M \sim 10^9\,M_\odot$ could display detectable deviations in future gravitational-wave measurements. The paper also discusses how these hairs provide a window into quantum gravity and could be probed by LISA observations of EMRIs via modified multipole structure and energy exchange.

Abstract

We consider black holes in Lorentz violating theories of massive gravity. We argue that in these theories black hole solutions are no longer universal and exhibit a large number of hairs. If they exist, these hairs probe the singularity inside the black hole providing a window into quantum gravity. The existence of these hairs can be tested by future gravitational wave observatories. We generically expect that the effects we discuss will be larger for the more massive black holes. In the simplest models the strength of the hairs is controlled by the same parameter that sets the mass of the graviton (tensor modes). Then the upper limit on this mass coming from the inferred gravitational radiation emitted by binary pulsars implies that hairs are likely to be suppressed for almost the entire mass range of the super-massive black holes in the centers of galaxies.

Bumpy black holes from spontaneous Lorentz violation

TL;DR

The work addresses whether black holes remain hairless in theories with spontaneous Lorentz violation and a massive graviton. It shows that instantaneous interactions in the Higgs phase generate an infinite set of BH hairs, making the exterior geometry sensitive to the interior and undermining the universality of the Kerr solution. The hair amplitude scales with the graviton mass parameter , so constraints on from binary pulsars strongly suppress observable bumps for most SMBHs, while the most massive systems with could display detectable deviations in future gravitational-wave measurements. The paper also discusses how these hairs provide a window into quantum gravity and could be probed by LISA observations of EMRIs via modified multipole structure and energy exchange.

Abstract

We consider black holes in Lorentz violating theories of massive gravity. We argue that in these theories black hole solutions are no longer universal and exhibit a large number of hairs. If they exist, these hairs probe the singularity inside the black hole providing a window into quantum gravity. The existence of these hairs can be tested by future gravitational wave observatories. We generically expect that the effects we discuss will be larger for the more massive black holes. In the simplest models the strength of the hairs is controlled by the same parameter that sets the mass of the graviton (tensor modes). Then the upper limit on this mass coming from the inferred gravitational radiation emitted by binary pulsars implies that hairs are likely to be suppressed for almost the entire mass range of the super-massive black holes in the centers of galaxies.

Paper Structure

This paper contains 2 sections, 8 equations, 2 figures.

Table of Contents

  1. Introduction and summary
  2. No-hair theorems

Figures (2)

  • Figure 1: In the presence of the spontaneous Lorentz breaking black holes can have different temperatures for different fields. This allows to perform thermodynamic transformations whose net effect is the transfer of heat $Q_2$ from a cold reservoir at temperature $T_2$ to a hotter one at temperature $T_1$ (left). Then one can close a cycle by feeding heat $Q_1$ at the higher temperature $T_1$ into a machine that produces work $W$ and as a byproduct releases heat $Q_2$ at the lower temperature $T_2$ (right). The net effect of the cycle is the conversion of heat into mechanical work.
  • Figure :