The agony of a solitary black hole lasts forever. But in its final moments, as its mass evaporates according to the law discovered by Hawking, it manages to send a radio farewell signal. Not a quantum whisper, but a classical hum — if only there's a magnetic field nearby. That's the scenario physicists have unpacked, envisioning the dying hole as a giant antenna that radiates not because something flows into it, but because the spacetime around it changes shape.
The key to the mechanism is a taut blanket: that's the Schwarzschild metric — the geometry of spacetime around a non-rotating black hole, first described by Schwarzschild in 1916. As long as the hole's mass stays constant, the blanket is static. But gravity gives the hole no rest: Hawking evaporation makes the mass melt away, and the blanket begins to oscillate. If threaded by magnetic field lines, these oscillations turn into electromagnetic waves. They rush outward, carrying away a tiny fraction of the hole's energy.
Mathematically, the effect is extracted from Maxwell's equations in curved spacetime. Using the Laplace transform, a kind of microscope for slowly varying processes, the authors decomposed the burst and obtained a spectrum. The spectrum turned out to be red: the radiation energy falls with frequency ω as $ω^{-8/3}$. Most energy is concentrated at frequencies on the order of 1/$τ_H$, where $τ_H$ is the hole's lifetime. For a hole with mass $10^{15}$ g, this corresponds to ultra-long radio waves with a period of fractions of a picosecond. The signal is clean: the electric and magnetic fields in the far zone are equal, orthogonal, and form a transverse electric (TE) mode, just like a plane wave in ordinary vacuum.
So classical spacetime curvature turns into an electromagnetic echo. It doesn't drown out quantum evaporation but adds a new observational tool. Primordial black holes, if they exist, could have survived to this day, fading away in residual cosmic magnetic fields. Their antenna signal, an ultra-weak but rigorously predicted emission, becomes another thread in unraveling dark matter. The theory needs refinement: hole rotation, self-consistent energy balance, collapse of asymmetric matter — all promise new nuances. But already, evaporation gains a second, classical dimension. The dying black hole becomes a transmitter, whose farewell song is written into the fabric of space itself.
If a black hole with the mass of an asteroid (~$10^{20}$ g) evaporated in Earth's magnetic field (0.5 G), the electromagnetic power would be just $10^{-30}$ of the Hawking power, but on the scale of the Universe, this could add up.