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

TL;DR

This paper analytically investigates how a black hole's event horizon affects the screening of a Proca (massive vector) field during dynamic collapse, challenging previous assumptions of adiabaticity and revealing implications for electromagnetic phenomena.

Contribution

It provides an analytical model of Proca field evolution during black hole formation without assuming adiabaticity, showing the screening process depends on black hole mass and affects observable electromagnetic effects.

Findings

Screening time scale is set by black hole mass.

Loss of Proca hair occurs on the same time scale as collapse.

Discontinuous jump between massive and massless electrodynamics at the horizon.

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. The latter conclusion disproves results of a number of papers. 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 gives rise to experimentally observed effects including generation of electric asymmetry of the Universe and galactic magnetic fields.