Electromagnetic field of a charge asymptotically approaching a spherically symmetric black hole

Abstract

We consider a test charged particle falling onto a Schwarzschild black hole and evaluate its electromagnetic field. The Regge-Wheeler equation is solved analytically by approximating the potential barrier with Dirac delta function and rectangular barrier. We show that for asymptotically large times measured by a distant observer the electromagnetic field approaches the spherically symmetric electrostatic field. This implies that in the region accessible to a distant observer the initial state of separated charge and the electromagnetic field outside the event horizon of Schwarzschild black hole becomes asymptotically indistinguishable from the Reisnner-Nordström solution. The implications of this result for some astrophysical models of black holes accreting charged particles are discussed.