TY - JOUR

T1 - Superradiant instability of black holes immersed in a magnetic field

AU - Brito, Richard

AU - Cardoso, Vitor

AU - Pani, Paolo

PY - 2014/5/27

Y1 - 2014/5/27

N2 - 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 similar to 1/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.

AB - 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 similar to 1/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.

KW - RELATIVISTIC MAGNETOHYDRODYNAMIC SIMULATIONS

KW - QUASI-NORMAL MODES

KW - PERTURBATIONS

KW - AMPLIFICATION

U2 - 10.1103/PhysRevD.89.104045

DO - 10.1103/PhysRevD.89.104045

M3 - Journal article

VL - 89

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 10

M1 - 104045

ER -