(Anti-)Evaporation of Schwarzschild-de Sitter Black Holes

TL;DR

The paper analyzes quantum evolution of Schwarzschild–de Sitter black holes near the maximal mass (Nariai) limit by a two‑dimensional dilaton gravity model with one‑loop quantum corrections in the large N limit. It identifies two perturbation channels: an anti‑evaporation mode where the horizon grows and an evaporation mode that shrinks it, with the latter activated by the radiation distribution or by boundary conditions. The no‑boundary condition for nucleated cosmological holes selects the evaporative channel, implying that neutral primordial SdS black holes in de Sitter space evaporate. Overall, the work reveals qualitatively new quantum gravitational behavior in cosmological black hole spacetimes and connects horizon dynamics to quantum boundary conditions.

Abstract

We study the quantum evolution of black holes immersed in a de Sitter background space. For black holes whose size is comparable to that of the cosmological horizon, this process differs significantly from the evaporation of asymptotically flat black holes. Our model includes the one-loop effective action in the s-wave and large N approximation. Black holes of the maximal mass are in equilibrium. Unexpectedly, we find that nearly maximal quantum Schwarzschild-de Sitter black holes anti-evaporate. However, there is a different perturbative mode that leads to evaporation. We show that this mode will always be excited when a pair of cosmological holes nucleates.