Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The Fate of Nucleated Black Holes in de Sitter Quantum Gravity

Xiaoyi Shi, Gustavo J. Turiaci, Chih-Hung Wu

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.

The Fate of Nucleated Black Holes in de Sitter Quantum Gravity

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.

Paper Structure

This paper contains 30 sections, 222 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The Nariai geometry and the gravitational path integral
  3. Hawking-Moss and the gravitational path integral
  4. Black-hole nucleation in de Sitter
  5. The homogeneous $(A,B)$ sector.
  6. Combining the Hawking-Moss process with the Nariai solution
  7. Black-hole nucleation in the false vacuum:
  8. Hawking-Moss decay:
  9. Black-hole nucleation in the true vacuum:
  10. Anatomy of the near-Nariai geometry: classical analysis
  11. The near-Nariai throat and two-dimensional dilaton gravity
  12. Near-Nariai perturbations and horizon diagnostics
  13. The evaporation of pair-created dS black holes
  14. The one-loop effective theory
  15. The thermal Hawking radiation of the near-Nariai black hole
  16. ...and 15 more sections

Figures (3)

  • Figure 1: Schematic scalar potential relevant for the Hawking--Moss transition.
  • Figure 2: Penrose diagram for a black hole in dS with mass $0<M<M_N$. We indicate the coordinates used in the text and the location of the horizons. The vertical lines have constant ${\sf r}$ or $\chi$. The horizontal lines have constant ${\sf t}$. $\mathcal{H}_c^\pm$ are located at $\chi=\pi$ or ${\sf r}=\infty$, while $\mathcal{H}_b^\pm$ are located at $\chi=0$ or ${\sf r}=-\infty$.
  • Figure 3: $\tau$ contour of the no-boundary geometry in our conventions.