Black holes turn white fast, otherwise stay black: no half measures

Abstract: Recently, various authors have proposed that the first ultraviolet effect on the gravitational collapse of massive stars to black holes is the transition between a black-hole geometry and a white-hole geometry, though their proposals are radically different in terms of their physical interpretation and characteristic time scales [1,2]. Several decades ago, it was shown by Eardley that white holes are highly unstable to the accretion of small amounts of matter, being rapidly turned into black holes [3]. Studying the crossing of null shells on geometries describing the black-hole to white-hole transition, we obtain the conditions for the instability to develop in terms of the parameters of these geometries. We conclude that transitions with long characteristic time scales are pathologically unstable: occasional perturbations away from the perfect vacuum around these compact objects, even if being imperceptibly small, suffocate the white hole explosion. On the other hand, geometries with short characteristic time scales are shown to be robust against perturbations, so that the corresponding processes could take place in real astrophysical scenarios. This motivates a conjecture about the transition amplitudes of different decay channels for black holes in a suitable ultraviolet completion of general relativity.