Superradiant instability of black holes immersed in a magnetic field

TL;DR

This paper investigates how magnetic fields around spinning black holes can cause superradiant instabilities, providing a detailed linear analysis of the Ernst spacetime and confirming the instability through scalar perturbations of magnetized Kerr--Newman black holes.

Contribution

First fully-consistent linear analysis of superradiant instability in Ernst spacetime, revealing magnetic fields' role in black hole spin limits and instability timescales.

Findings

Magnetic fields can trigger superradiant instabilities in black holes.

The instability timescale can be much shorter than for massive bosonic fields.

Strong magnetic fields impose an upper limit on black hole spin.

Abstract

Magnetic fields surrounding spinning black holes can confine radiation and trigger superradiant instabilities. To investigate this effect, we perform the first fully-consistent linear analysis of the Ernst spacetime, an exact solution of the Einstein--Maxwell equations describing a black hole immersed in a uniform magnetic field $B$. In the limit in which the black-hole mass vanishes, the background reduces to the marginally stable Melvin spacetime. The presence of an event horizon introduces a small dissipative term, resulting in a set of long-lived -- or unstable -- modes. We provide a simple interpretation of the mode spectrum in terms of a small perfect absorber immersed in a confining box of size $\sim1/B$ and show that rotation triggers a superradiant instability. By studying scalar perturbations of a magnetized Kerr--Newman black hole, we are able to confirm and quantify the details of this instability. The instability time scale can be orders of magnitude shorter than that associated to massive bosonic fields. The instability extracts angular momentum from the event horizon, competing against accretion. This implies that strong magnetic fields set an upper bound on the black-hole spin. Conversely, observations of highly-spinning massive black holes impose an intrinsic limit to the strength of the surrounding magnetic field. We discuss the astrophysical implications of our results and the limitations of the Ernst spacetime to describe realistic astrophysical configurations.