The Timescale for Loss of Massive Vector Hair by a Black Hole and its Consequences for Proton Decay

TL;DR

This paper analyzes the timescale for black holes to lose massive gauge field hair, linking it to the symmetry breaking scale, and discusses implications for proton decay and black hole physics.

Contribution

It introduces a new understanding of the timescale for gauge field hair loss in black holes based on the gauge boson Compton wavelength, impacting theories of proton stability.

Findings

Black holes radiate gauge field hair on a timescale inversely proportional to the gauge boson mass.

Below a certain black hole mass, Hawking radiation discharges the black hole faster than gauge hair loss.

Implications for proton decay suppression via gravitational effects are discussed.

Abstract

It has long been known that matter charged under a broken U(1) gauge symmetry collapsing to form a black hole will radiate away the associated external (massive) gauge field. We show that the timescale for the radiation of the monopole component of the field will be on the order of the inverse Compton wavelength of the gauge boson (assuming natural units). Since the Compton wavelength for a massive gauge boson is directly related to the scale of symmetry breaking, the timescale for a black hole to lose its gauge field "hair" is determined only by this scale. The timescale for Hawking radiation, however, is set by the mass of the black hole. These different dependencies mean that for any (sub-Planckian) scale of symmetry breaking we can define a mass below which black holes radiate quickly enough to discharge themselves via the Hawking process before the gauge field is radiated away. This has important implications for the extrapolation of classical black hole physics to Planck-scale virtual black holes. In particular, we comment on the implications for protecting protons from gravitationally mediated decay.