Scalar clouds in charged stringy black hole-mirror system

TL;DR

This paper investigates the formation of scalar clouds around charged stringy black holes with a mirror boundary, providing analytical and numerical results for the conditions and locations where these clouds can exist.

Contribution

It introduces the study of scalar clouds in charged stringy black holes with mirror boundaries, including analytical solutions for cloud locations in the high charge regime.

Findings

Scalar clouds exist only at specific mirror locations.

Analytical mirror locations match numerical results.

Clouds can form near the black hole horizon.

Abstract

It is reported that massive scalar fields can form bound states around Kerr black holes [C. Herdeiro, and E. Radu, Phys. Rev. Lett. 112, 221101 (2014)]. These bound states are called scalar clouds, which have a real frequency $\omega=m\Omega_H$, where $m$ is the azimuthal index and $\Omega_H$ is the horizon angular velocity of Kerr black hole. In this paper, we study scalar clouds in a spherically symmetric background, i.e. charged stringy black holes, with the mirror-like boundary condition. These bound states satisfy the superradiant critical frequency condition $\omega=q\Phi_H$ for the charged scalar field, where $q$ is the charge of scalar field, and $\Phi_H$ is the horizon electrostatic potential. We show that, for the specific set of black hole and scalar field parameters, the clouds are only possible for the specific mirror locations $r_m$. It is shown that the analytical results of mirror location $r_m$ for the clouds are perfectly coincide with the numerical results. We also show that the scalar clouds are also possible when the mirror locations are close to the horizon. At last, we provide an analytical calculation of the specific mirror locations $r_m$ for the scalar clouds in the $qQ\gg 1$ regime.