Cherenkov emission by a fast-moving uncharged Schwarzschild black hole

Abstract

We demonstrate that, in the presence of an external magnetic field, an uncharged classical Schwarzschild black hole moving superluminally in a dielectric with permittivity $\epsilon >1$ produces Cherenkov emission. This is a new physical effect: classical (non-quantum) emission of electromagnetic waves by a completely charge-neutral ``particle.'' The governing equations (involving general relativity, electromagnetism, and the physics of continuous media) have no external electromagnetic source -- it is the distortion of the initial electromagnetic fields by the gravity of the black hole that plays the role of a superluminally moving source. The effect relies on nonzero values of both the magnetic field and the gravitational radius, as well as on the usual Cherenkov condition on the velocity, $v/c>1/\sqrt{\epsilon }$. Unlike Cherenkov emission by a point charge, the effective source in this case is spatially distributed, with emission generated along the single Cherenkov emission cone. The emitted spectrum is red-dominated, with power $\propto d{k}_z/|k_z|$ for wave numbers $|k_z|\le 1/R_G$, where $R_G$ is the Schwarzschild radius. We comment on possible observability of this process during black hole -- neutron star mergers.