The Fate of Nucleated Black Holes in de Sitter Quantum Gravity

TL;DR

This paper rigorously analyzes the nucleation and evolution of black holes in de Sitter space, confirming the instanton interpretation, exploring scalar field effects, and demonstrating standard evaporation back to vacuum.

Contribution

It provides a firmer foundation for the Nariai instanton interpretation, examines scalar field influence on nucleation, and clarifies black hole evolution as standard Hawking evaporation.

Findings

Scalar fields can enhance black-hole nucleation rates.

The anti-evaporation scenario is unphysical due to singular horizons.

Black holes fully evaporate back to de Sitter vacuum, consistent with Boltzmann fluctuations.

Abstract

The Euclidean Nariai geometry has long been proposed as the instanton describing the nucleation of maximal-mass black holes in de Sitter space. We place this interpretation on firmer footing by showing that, once an observer is included, the gravitational path integral produces the imaginary phase required for a transition rate. As a warmup, we revisit the Hawking-Moss instanton and, as a byproduct, find that scalar fields can enhance black-hole nucleation, suggesting a quantum-gravity bound on scalar potentials with de Sitter solutions. We then study the subsequent semiclassical evolution of the nucleated black hole. We show that the previously claimed "anti-evaporation" channel is unphysical, arising from a quantum state with singular horizons. In a smooth state, the black hole instead undergoes standard thermal Hawking evaporation. We verify explicit agreement with the no-boundary state and argue that this evaporation is not subject to large quantum-gravity corrections. The nucleated black hole thus evaporates completely back to the maximally-entropic empty de Sitter vacuum, making the full process a Boltzmann fluctuation.