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

Black holes in d < 3 spatial dimensions are studied from the perspective of the corpuscu- lar 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 Hawk- ing evaporation. We show that the occupation number of gravitons in the condensate scales holographically in all dimensions as Nd ∼ (Ld/lp)d−1, where Ld is the relevant length for the system in the (1 + d)-dimensional spacetime. In particular, this analysis shows that black holes cannot contain more than a few gravitons in d = 1. Since dimen- sional 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 (1 + 1)-dimensional cosmology in the context of corpuscular gravity and show that the Friedmann equation reproduces the expected holographic scaling as in higher dimensions.