Evaporation of black holes via radiation predicted by Hawking remains unobserved, but any additional electromagnetic emission could change the picture. Astrophysical black holes often sit in magnetic fields, so the interaction of evaporating geometry with these fields is a natural process that hadn't been fully considered before.
The authors considered a weak external magnetic field in vacuum around a non-rotating Schwarzschild black hole with a variable mass following Hawking's law. Using a 3+1 decomposition and a Laplace approach, they derived an effective source term in Maxwell's equations arising from radial energy redistribution. A key element was applying the retarded Green's function, which automatically selects outgoing waves and fixes the causal arrow of radiation.
The main result: the spectral energy of the radiation dE/dω ∝ B0^2 m0^2 τH^{-2/3} $ω^{-8/3}$ — a red spectrum, with energy concentrated at frequencies around the inverse evaporation timescale. The electric and magnetic fields in the far zone are equal and orthogonal to the direction of propagation, forming a transverse electric (TE) mode. The total radiated energy over the black hole lifetime is EB ≈ 0,2 B0^2 RSch^2 c τH, which always remains a small correction to the Hawking energy for realistic parameters. For instance, for a black hole with mass $10^{15}$ g in a 1 G field, the ratio EB/EH ≈ $10^{-93}$ m0^4, ensuring the theory's applicability. No burst occurs at the end of evaporation — the radiation fades smoothly.
The work introduces a fundamentally new classical energy-loss channel: gravity non-quantum mechanically generates electromagnetic waves by deforming an external field. This effect is akin to a transmission line, with the evaporating geometry acting as a distributed generator and the magnetic field as the load. It echoes the Gertsenshtein-Zel'dovich effect, but here the source is not an incoming gravitational wave but the changing metric itself.
The model can be extended to rotating black holes, where frame-dragging and the magnetosphere modify the source. A self-consistent treatment of the back-reaction of electromagnetic radiation on the evaporation rate will be needed. Another avenue is studying spherical collapse and accretion, where a variable mass also triggers radiation.
The results are important for astrophysics of primordial black holes, which may evaporate in the early magnetic fields of the Universe, and for general field theory — as an example of radiation emerging from vacuum under non-stationary gravity.
Test the predictions via numerical simulations within general relativity with magnetic fields. Search for observational signatures of low-frequency TE waves from candidate evaporating black holes.
The paper touches on the black hole information paradox by offering an additional radiation channel, and demonstrates the interplay between gravitational and electromagnetic dynamics, which is relevant for quantum gravity theories.
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What the work does
The authors considered a non-rotating black hole with a variable mass in a weak external magnetic field. Using a 3+1 decomposition and a retarded Green's function, they derived an effective source in Maxwell's equations and obtained the spectrum of secondary electromagnetic radiation proportional to B0^2 m0^2 τ_H^{-2/3} ω^{-8/3}. The radiation turned out to be a transverse-electric mode with no final flare.
Where its strength is
This work introduces a new classical energy-loss channel: the changing spacetime geometry itself serves as a source of electromagnetic waves, requiring no charges. This opens up the possibility of detecting black hole evaporation through secondary radio emission, even if the primary Hawking radiation is too faint.
Where it could go next
Worth trying
Why this may matter
If secondary electromagnetic radiation indeed exists, it could become a new window into the physics of quantum evaporation, especially for primordial black holes, where other channels are unobservable.
Nearby works in our archive
The closest work in the archive sits at 0.68 by meaning — the usual level for our corpus.
If an asteroid-mass black hole (~$10^{20}$ g) were evaporating in Earth's magnetic field (0,5 G), its electromagnetic power would be just $10^{-30}$ of the Hawking power — but on cosmic scales, this could add up.