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On the Euclidean Action of de Sitter Black Holes and Constrained Instantons
by Edward K. Morvan, Jan Pieter van der Schaar, Manus R. Visser
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Submission summary
| Authors (as registered SciPost users): | Manus Visser · Jan Pieter van der Schaar |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2203.06155v3 (pdf) |
| Date accepted: | 2022-10-27 |
| Date submitted: | 2022-09-20 15:29 |
| Submitted by: | van der Schaar, Jan Pieter |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We compute the on-shell Euclidean action of Schwarzschild-de Sitter black holes, and take their contributions in the gravitational path integral into account using the formalism of constrained instantons. Although Euclidean de Sitter black hole geometries have conical singularities for generic masses, their on-shell action is finite and is shown to be independent of the Euclidean time periodicity and equal to minus the sum of the black hole and cosmological horizon entropy. We apply this result to compute the probability for a nonrotating, neutral arbitrary mass black hole to nucleate spontaneously in empty de Sitter space, which separates into a constant and a "non-perturbative" contribution, the latter corresponding to the proper saddle-point instanton in the Nariai limit. We also speculate on some further applications of our results, most notably as potential non-perturbative corrections to correlators in the de Sitter vacuum.
Author comments upon resubmission
List of changes
- We have moved some citations in the introduction to the more appropriate place.
- We have added several small clarifications and slightly improved the writing in several places
- We fixed a typo in the caption of figure 6.
- We removed the term 'mild singularities' on page 9 and rephrased what we actually mean.
- We extended the discussion of the application of constrained instantons. In particular, we have also clarified our remark regarding the smooth nature of the solutions.
- We added a footnote explaining that the linear fit can be understood as a large d expansion and that we neglected higher order terms.
- We have added some references
Published as SciPost Phys. 14, 022 (2023)