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Entropy of causal diamond ensembles

by Ted Jacobson, Manus R. Visser

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Submission summary

Authors (as registered SciPost users): Manus Visser
Submission information
Preprint Link: scipost_202303_00042v2  (pdf)
Date accepted: 2023-05-30
Date submitted: 2023-04-23 21:26
Submitted by: Visser, Manus
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Gravitation, Cosmology and Astroparticle Physics
  • High-Energy Physics - Theory
  • Quantum Physics
Approach: Theoretical


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.

List of changes

We have replaced the opening of section 2.1 with text that addresses the issue of boundary conditions.

Published as SciPost Phys. 15, 023 (2023)

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