Electromagnetic Emission from a Black Hole Evaporating in External Magnetic Field

Abstract

We describe a classical (non-quantum) radiation process: additional (to Hawking) emission by a black hole evaporating in an external magnetic field in vacuum. The electromagnetic radiation process is completely electric charge-free and bears some resemblance to the Gertsenshtein-Zel'dovich effect. The time evolution of the spacetime metric perturbs a static background magnetic field, inducing a radiative field that acts as an effective electromagnetic source even in the absence of physical charges or currents. To isolate the dynamic effects of the time-dependent spacetime on the external magnetic field, we approximate Hawking radiation as a spherically symmetric outflow of null fluid governed by the prescribed time-dependence of the central mass $M(t)$. We employ Laplace transform, which selects the retarded outgoing branch of the electromagnetic response, producing fields proportional to $\Theta(t-r)$ and thereby fixing a causal radiative arrow of emission. The emitted spectral energy is red-dominated, scaling as $d\mathcal{E}_B/d\omega \propto B_0^2 m_0^2 \tau_H^{-2/3} \omega^{-8/3}$, where $\tau_H$ is the Hawking evaporation timescale, and corresponds to a pure Transverse Electric (TE) mode. There is no final bright burst at the end of the evaporation. We offer classical analogues for this mechanism as transmission-line emission and, separately, as the displacement current emission from a medium with time-varying dielectric permittivity.