The gravitational Vavilov-Cherenkov effect

In this letter we show that an uncharged black hole moving superluminally in a transparent dielectric medium violates Hawking's area theorem. The violation can be overcome through the emission of radiation. Since modes cannot emerge from the black hole itself, this radiation must originate from a collective effect in the medium, in complete analogy with the Vavilov-Cherenkov effect. However, because the black hole is uncharged, the emission mechanism must be different. We discuss the physical origin of the effect and obtain a Newtonian estimation. Then we obtain the appropriate equations in the relativistic case and show that the field which is radiated away is a combination of gravitational and electromagnetic degrees of freedom. Possible astrophysical relevance for the detection of primordial black holes and binary systems is discussed.