Quasi-bound state resonances of charged massive scalar fields in the near-extremal Reissner\u2013Nordstr\xf6m black-hole spacetime

Shahar Hod

doi:10.1140/epjc/s10052-017-4920-8

Abstract

The quasi-bound states of charged massive scalar fields in the near-extremal charged Reissner–Nordström black-hole spacetime are studied analytically. These discrete resonant modes of the composed black-hole-field system are characterized by the physically motivated boundary condition of ingoing waves at the black-hole horizon and exponentially decaying (bounded) radial eigenfunctions at spatial infinity. Solving the Klein–Gordon wave equation for the linearized scalar fields in the black-hole spacetime, we derive a remarkably compact analytical formula for the complex frequency spectrum which characterizes the quasi-bound state resonances of the composed Reissner–Nordström-black-hole-charged-massive-scalar-field system.

Highlights

The powerful no-hair theorems of Bekenstein and Mayo [1]1 have revealed the fact that, in asymptotically flat spacetimes, spherically symmetric charged black holes cannot support external static matter configurations made of charged massive scalar fields
The main goal of the present paper is to explore the physical properties of these quasi-bound state charged matter configurations in the Reissner–Nordström black-hole spacetime
Remembering that the quasi-bound configurations of the charged massive scalar fields in the charged Reissner–Nordström black-hole spacetime are characterized by exponentially decaying radial eigenfunctions at spatial infinity [see Eqs. (10) and (11)], one arrives at the important conclusion that the coefficient of the exploding exponent e x in the asymptotic spatial expression (31) should vanish: N1 × (2 )−κ

Summary

Introduction

The powerful no-hair theorems of Bekenstein and Mayo [1] (see [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]) have revealed the fact that, in asymptotically flat spacetimes, spherically symmetric charged black holes cannot support external static matter configurations made of charged massive scalar fields. The main goal of the present paper is to explore the physical properties of these quasi-bound state charged matter configurations in the Reissner–Nordström black-hole spacetime To this end, we shall analyze the Klein–Gordon wave equation for the charged massive scalar fields in the charged black-hole spacetime. As we shall explicitly show below, in the extremal Q/M → 1 limit of the central charged black hole, one can derive a remarkably compact analytical formula for the discrete frequency spectrum which characterizes the quasi-bound state resonances of the composed Reissner–Nordström-black-hole-chargedmassive-scalar-field configurations

Description of the system

Summary