Time scale for loss of massive vector hair by a black hole and its consequences for proton decay

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.

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

“…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. Thus, according to the results of [12], the prediction of [11] is correct at least in the monopole case.…”

“…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, therefore, the result of [12] is incorrect. We analytically calculate the evolution of the field of the uniformly charged spherical shell surrounding the BH and contracting according to some undefined law.…”

“…Strictly speaking, the results obtained above are valid for the eternal BH and now we will discuss the influence of replacing this idealized source of gravity by a more realistic gravitating object formed as a result of the collapse. 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. However, the results of our calculations show that this is not the case.…”

“…An attempt to prove the statement of [11] was made in [12]. 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.…”

New test on the Einstein equivalence principle through the photon ring of black holes

“…Possibility of violation of the EEP near a black hole could be suggested by the superradiance process of rotating black holes [62][63][64][65][66], which implies there might be a fruitful environment of light particles around rotating black holes at horizon scale [67][68][69][70][71][72][73]. Moreover, if these particles are those beyond the standard model and are coupled to photons, there might be a phenomenological violation of EEP.…”