Effective photon mass from black-hole formation

TL;DR

This paper calculates the effective photon mass near small black holes due to quantum effects, compares it with plasma effects, and estimates black hole proximity based on photon mass bounds, showing negligible corrections to fundamental constants.

Contribution

It provides the first computation of effective photon mass in QED near small black holes and compares black-hole effects with plasma phenomena.

Findings

Effective photon mass is influenced by black-hole presence.

Black-hole effects on electron mass and fine structure constant are negligible.

Estimated proximity to black holes based on photon mass bounds.

Abstract

We compute the value of effective photon mass $m_\gamma$ at one-loop level in QED in the background of small ($10^{10}\,\text{g} \lesssim M \ll 10^{16}\,\text{g}$) spherically symmetric black hole in asymptotically flat spacetime. This effect is associated with the modification of electron/positron propagator in presence of event horizon. Physical manifestations of black-hole environment are compared with those of hot neutral plasma. We estimate the distance to the nearest black hole from the upper bound on $m_\gamma$ obtained in the Coulomb-law test. We also find that corrections to electron mass $m_e$ and fine structure constant $\alpha$ at one-loop level in QED are negligible in the weak gravity regime.