On the Euclidean Action of de Sitter Black Holes and Constrained Instantons
arXiv:2203.06155 · doi:10.21468/SciPostPhys.14.2.022
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.
arXiv comment34 pages, 15 figures, added further references and clarifications. Revised version for SciPost
References in corpus (58)
- Eternal Black Holes in AdS
- The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
- Emergent Gravity and the Dark Universe
- Entanglement entropy of black holes
- Entropy, Area, and Black Hole Pairs
- Quantum Gravity In De Sitter Space
- Mass, Entropy and Holography in Asymptotically de Sitter Spaces
- Thermodynamic Volumes and Isoperimetric Inequalities for de Sitter Black Holes
- The Trouble with de Sitter Space
- Positive vacuum energy and the N-bound
- Pair Creation of Black Holes During Inflation
- Thermodynamics of de Sitter Black Holes: Thermal Cosmological Constant
- Cosmological Breaking of Supersymmetry?
- Black Hole Entropy and the Dimensional Continuation of the Gauss-Bonnet Theorem
- Cosmological Multi-Black Hole Solutions
- On Pair Creation of Extremal Black Holes and Kaluza-Klein Monopoles
- (Anti-)Evaporation of Schwarzschild-de Sitter Black Holes
- Cosmological production of charged black hole pairs
- Temperature and entropy of Schwarzschild-de Sitter space-time
- Black holes as bubble nucleation sites
- De Sitter Musings
- Mechanical First Law of Black Hole Spacetimes with Cosmological Constant and Its Application to Schwarzschild-de Sitter Spacetime
- Vacuum metastability with black holes
- Thermodynamics of horizons: de Sitter black holes and reentrant phase transitions
- Bekenstein bounds in de Sitter and flat space
- Low-dimensional de Sitter quantum gravity
- Towards a quantum theory of de Sitter space
- Entropy in Black Hole Pair Production
- Action, Mass and Entropy of Schwarzschild-de Sitter black holes and the de Sitter/CFT Correspondence
- Nariai, Bertotti-Robinson and anti-Nariai solutions in higher dimensions
- Festina Lente: EFT Constraints from Charged Black Hole Evaporation in de Sitter
- de Sitter Black Holes with Either of the Two Horizons as a Boundary
- Area products for stationary black hole horizons
- Gravitational Thermodynamics of Causal Diamonds in (A)dS
- Quasi-local energy and microcanonical entropy in two-dimensional nearly de Sitter gravity
- Concept of temperature in multi-horizon spacetimes: Analysis of Schwarzschild-De Sitter metric
- Wormholes and black hole microstates in AdS/CFT
- Gravitational Constrained Instantons
- Black hole pair creation in de Sitter space: a complete one-loop analysis
- Quantum Global Structure of de Sitter Space
- Proliferation of de Sitter Space
- A note on entropy of de Sitter black holes
- Effective Temperatures and Radiation Spectra for a Higher-Dimensional Schwarzschild-de-Sitter Black-Hole
- Upper bound for entropy in asymptotically de Sitter space-time
- Lorentzian Condition in Quantum Gravity
- Quasilocal Thermodynamics of Kerr de Sitter Spacetimes and the dS/CFT Correspondence
- De Sitter Gravity and Liouville Theory
- Aspects of Quantum Gravity in de Sitter Spaces
- Schottky Anomaly of deSitter Black Holes
- Gravitational Thermodynamics of Schwarzschild-de Sitter Space
- Black Hole and Cosmological Particle Production in Schwarzschild de Sitter
- Particle creation by de Sitter black holes revisited
- de Sitter thermodynamics in the canonical ensemble
- Black Holes in de Sitter Space: Masses, Energies and Entropy Bounds
- Euclidean de Sitter Black Holes and Microcanonical Equilibrium
- Emergent Gravity in a Holographic Universe
- Black Holes Hint Towards De Sitter-Matrix Theory
- Holographic Space-time, Newton`s Law, and the Dynamics of Horizons