SciPost Physics

SciPost Phys. 15, 023 (2023) · published 24 July 2023

• doi: 10.21468/SciPostPhys.15.1.023
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Abstract

We define a canonical ensemble for a gravitational causal diamond by introducing an artificial York boundary inside the diamond with a fixed induced metric and temperature, and evaluate the partition function using a saddle point approximation. For Einstein gravity with zero cosmological constant there is no exact saddle with a horizon, however the portion of the Euclidean diamond enclosed by the boundary arises as an approximate saddle in the high-temperature regime, in which the saddle horizon approaches the boundary. This high-temperature partition function provides a statistical interpretation of the recent calculation of Banks, Draper and Farkas, in which the entropy of causal diamonds is recovered from a boundary term in the on-shell Euclidean action. In contrast, with a positive cosmological constant, as well as in Jackiw-Teitelboim gravity with or without a cosmological constant, an exact saddle exists with a finite boundary temperature, but in these cases the causal diamond is determined by the saddle rather than being selected a priori.

• Perez et al., Light-cone thermodynamics: Purification of the Minkowski vacuum
  Phys. Rev. D 109, 125012 (2024) [Crossref]
• Lemos et al., Black holes and hot shells in the Euclidean path integral approach to quantum gravity
  Class. Quantum Grav. 40, 235012 (2023) [Crossref]
• Edwards, A functional contextual, observer-centric, quantum mechanical, and neuro-symbolic approach to solving the alignment problem of artificial general intelligence: safe AI through intersecting computational psychological neuroscience and LLM architecture for emergent theory of mind
  Front. Comput. Neurosci. 18, 1395901 (2024) [Crossref]
• Kaloper, Axion flux monodromy discharges relax the cosmological constant
  J. Cosmol. Astropart. Phys. 2023, 032 (2023) [Crossref]
• Alonso-Serrano et al., Emergence of quadratic gravity from entanglement equilibrium
  Phys. Rev. D 108, 084057 (2023) [Crossref]
• A et al., Quantum theory of three-dimensional de Sitter space
  Phys. Rev. D 109, 025011 (2024) [Crossref]
• Lemos et al., Hot spaces with positive cosmological constant in the canonical ensemble: de Sitter solution, Schwarzschild–de Sitter black hole, and Nariai universe
  Phys. Rev. D 109, 084016 (2024) [Crossref]