Effective photon mass from black-hole formation

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.