On dynamic aspects of the Proca field screening by a black hole

Andrei L Erofeev

doi:10.1140/epjc/s10052-020-8044-1

Abstract

Classical black holes are known for almost half a century to nullify exterior classical massive vector field associated with a charge crossing the event horizon. This implies that, from the point of view of an external observer, the Proca field of the charge is screened with the strength gradually increasing as the charge adiabatically approaches the event horizon. In this paper we reject the adiabaticity constraint and calculate analytically the field evolution with respect to a distant observer in the frame of the simplest model of a contracting charged spherical shell concentrically surrounding a Schwarzschild black hole. We show that a time scale of the screening is determined by a mass of the black hole and, moreover, loss of Proca hair during the collapse of charged matter has the same temporal character. Due to existence of the event horizon, there is discontinuous jump between massive and massless electrodynamics. This means that presence of an arbitrarily small mass of the photon induces observable effects, which include generation of electric asymmetry of the Universe and galactic magnetic fields.

Highlights

The absence of massive vector fields associated with black holes (BH) is a particular conclusion of no-hair theorems proved by Bekenstein and Teitelboim
In this paper we show that the time scale of the screening and the Proca hair loss is equal in order of magnitude to the gravitational radius of the BH and, the result of
According to the work [12], if a charged star collapses into a BH, the exterior massive vector field associated with the charge of the star decays over time of the order of 1/m

Summary

Introduction

The absence of massive vector fields associated with black holes (BH) is a particular conclusion of no-hair theorems proved by Bekenstein and Teitelboim. The author of this paper concluded that the monopole massive vector field created by spherically symmetric distribution of charged matter collapsing into a Schwarzschild BH does have the decay time scale governed by the Compton wavelength of the corresponding gauge boson. BHs with nonzero angular momentum were found in [20] to be able to possess massive vector hair, but that has a harmonic temporal dependence and is not continuously connected with the Kerr-Newman solution This hairy behavior is not directly related to the problem of electrogenesis. It is natural to expect in this context that the qualitative picture of the field evolution in the limit of a small photon mass coincides with that for the Schwarzschild case, because axisymmetric BHs do not have massive vector hair that respect space-time symmetry. We conclude the article by summary of the results noting open areas for further research

Static solution of the Proca equation

Analytical calculation of the field evolution

Summary and conclusion