Electromagnetic field of a charge asymptotically approaching 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 time measured by a distant observer the electromagnetic field approaches the spherically symmetric electrostatic field exponentially fast. This implies that in the region accessible to a distant observer the initial state of separated charge and Schwarzschild black hole becomes asymptotically indistinguishable from the Reisnner-Nordström solution. Implications of this result for models with plasma accretion on black holes are discussed.7 a

7 pages, 2 figures

References in corpus (8)

• First-Principles Plasma Simulations of Black-Hole Jet Launching
• Exact Solutions of Regge-Wheeler Equation and Quasi-Normal Modes of Compact Objects
• Black Hole Pulsar
• Gravitomagnetic interaction of a Kerr black hole with a magnetic field as the source of the jetted GeV radiation of gamma-ray bursts
• Electromagnetic radiation from collisions at almost the speed of light: an extremely relativistic charged particle falling into a Schwarzschild black hole
• Can the BZ mechanism power steady jets?
• Spectrum of the radiation from electric charges and from dipoles which free infall into a black hole
• Electromagnetic radiation generated by a charged particle falling radially into a Schwarzschild black hole: A complex angular momentum description