Stationary scalar clouds around a rotating BTZ-like black hole in the Einstein-bumblebee gravity

TL;DR

This paper investigates stationary scalar clouds around a rotating BTZ-like black hole in Einstein-bumblebee gravity, revealing how Lorentz symmetry breaking influences cloud existence and superradiant instabilities.

Contribution

It demonstrates the existence of fundamental stationary scalar clouds in Einstein-bumblebee gravity and analyzes the effects of Lorentz symmetry breaking on these clouds and related instabilities.

Findings

Fundamental scalar clouds exist with overtone number n=0.

Lorentz symmetry breaking parameter s influences scalar clouds but not superradiance.

Superradiant instabilities occur only for fundamental modes.

Abstract

We have studied stationary clouds of massive scalar fields around a rotating BTZ-like black hole in the Einstein-bumblebee gravity, by imposing the Robin type boundary conditions at the AdS boundary. We establish, by scanning the parameter space, the existence of \textit{fundamental} stationary scalar clouds ($i.e.$, the overtone number $n=0$). In particular, we observe that the Lorentz symmetry breaking parameter $s$ and the quantum number $k$ play an opposite role in determining scalar clouds, which indicates the existence of \textit{degenerate} scalar clouds. To illustrate the fact that scalar clouds may only be supported for the $n=0$ case, we have analyzed the impact of various parameters on scalar quasinormal modes. It is shown that the Lorentz symmetry breaking parameter $s$ does not change the superradiance condition, and superradiant instabilities only appear for the fundamental modes. Our work shows that the Lorentz symmetry breaking provides richer physics in stationary scalar clouds around black holes.