Superradiant instability of a Kerr-like black hole in Einstein-bumblebee gravity

Rui Jiang, Rui-Hui Lin, and Xiang-Hua Zhai
Phys. Rev. D 104, 124004 – Published 1 December 2021

Abstract

An exact Kerr-like solution has been obtained recently in Einstein-bumblebee gravity model where Lorentz symmetry is spontaneously broken. In this paper, we investigate the superradiant instability of the Kerr-like black hole under the perturbation of a massive scalar field. We find the Lorentz breaking parameter L does not affect the superradiance regime or the regime of the bound states. However, since L appears in the metric and its effect cannot be erased by redefining the rotation parameter a˜=1+La, it indeed affects the bound state spectrum and the superradiance. We calculate the bound state spectrum via the continued-fraction method and show the influence of L on the maximum binding energy and the damping rate. The superradiant instability could occur since the superradiance condition and the bound state condition could be both satisfied. Compared with Kerr black hole, the nature of the superradiant instability of this black hole depends nonmonotonously not only on the rotation parameter of the black hole a˜ and the product of the black hole mass M and the field mass μ, but also on the Lorentz breaking parameter L. Through the Monte Carlo method, we find that for the l=m=1 state the most unstable mode occurs at L=0.79637, a˜/M=0.99884, and Mμ=0.43920, with the maximum growth rate of the field ωIM=1.676×106, which is about 10 times than that in the Kerr black hole.

  • Figure
  • Figure
  • Figure
  • Received 10 August 2021
  • Accepted 4 November 2021

DOI:https://doi.org/10.1103/PhysRevD.104.124004

© 2021 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Rui Jiang, Rui-Hui Lin*, and Xiang-Hua Zhai

  • Division of Mathematics and Theoretical Physics, Shanghai Normal University, 100 Guilin Road, Shanghai 200234, China

  • *linrh@shnu.edu.cn
  • zhaixh@shnu.edu.cn

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 104, Iss. 12 — 15 December 2021

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×