Entropy of causal diamond ensembles

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.

15 pages, 3 figures, v4: clarified reasoning, published version

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Cited by in corpus (6)

• Quantum theory of three-dimensional de Sitter space
• Thermodynamics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime
• From spacetime thermodynamics to Weyl transverse gravity
• Path integral derivation of the thermofield double state in causal diamonds
• Emergence of quadratic gravity from entanglement equilibrium
• Gravity from thermodynamics in vacuum: Lorentz invariance and the role of Bel-Robinson tensor