Lower dimensional corpuscular gravity and the end of black hole evaporation

TL;DR

This paper explores black holes in lower dimensions using a corpuscular model, revealing how graviton occupation scales holographically and providing insights into the end stages of Hawking evaporation.

Contribution

It demonstrates the holographic scaling of graviton occupation in lower-dimensional black holes and connects these findings to quantum gravity models and black hole evaporation.

Findings

Graviton occupation number scales holographically as N_d ∼ (L_d/ℓ_p)^{d-1}

Black holes in d=1 contain only a few gravitons

Friedmann equation in (1+1)D cosmology reproduces holographic scaling

Abstract

Black holes in $d < 3$ spatial dimensions are studied from the perspective of the corpuscular model of gravitation, in which black holes are described as Bose-Einstein condensates 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 $N_d \sim \left(L_d/\ell_{\rm p}\right)^{d-1}$, where $L_d$ is the relevant length for the system in the $(1+d)$-dimensional space-time. In particular, this analysis shows that black holes cannot contain more than a few gravitons in $d=1$. 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 $(1+1)$-dimensional cosmology in the context of corpuscular gravity, and show that the Friedmann equation reproduces the expected holographic scaling as in higher dimensions.