Superradiance of a charged scalar field coupled to the Einstein-Maxwell equations

TL;DR

This paper numerically studies superradiance phenomena in a charged scalar field interacting with a Reissner-Nordström black hole, revealing mass and charge loss and analyzing late-time decay in an asymptotically flat spacetime.

Contribution

It introduces a hyperboloidal evolution scheme to simulate superradiance in the Einstein-Maxwell-Klein-Gordon system and derives a Bondi mass loss formula.

Findings

Superradiance causes significant black hole mass and charge reduction.

Numerical simulations confirm superradiant amplification at specific frequencies.

Late-time decay of scalar field analyzed using derived formulas.

Abstract

We consider the Einstein-Maxwell-Klein-Gordon equations for a spherically symmetric scalar field scattering off a Reissner-Nordstr\"om black hole in asymptotically flat spacetime. The equations are solved numerically using a hyperboloidal evolution scheme. For suitable frequencies of the initial data, superradiance is observed, leading to a substantial decrease of mass and charge of the black hole. We also derive a Bondi mass loss formula using the Kodama vector field and investigate the late-time decay of the scalar field.