Lower-dimensional corpuscular gravity and the end of black hole evaporation

Abstract

Black holes in [Formula: see text] spatial dimensions are studied from the perspective of the corpuscular model of gravitation, in which black holes are described as Bose–Einstein condensates (BEC) of (virtual soft) gravitons. In particular, since the energy of these gravitons should increase as the black hole evaporates, eventually approaching the Planck scale, the lower-dimensional cases could provide important insight into the late stages and end of Hawking evaporation. We show that the occupation number of gravitons in the condensate scales holographically in all dimensions as [Formula: see text], where [Formula: see text] is the relevant length for the system in the [Formula: see text]-dimensional spacetime. In particular, this analysis shows that black holes cannot contain more than a few gravitons in [Formula: see text]. Since dimensional reduction is a common feature of many models of quantum gravity, this result can shed light on the end of the Hawking evaporation. We also consider [Formula: see text]-dimensional cosmology in the context of corpuscular gravity and show that the Friedmann equation reproduces the expected holographic scaling as in higher dimensions.