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Entropy of causal diamond ensembles
by Ted Jacobson, Manus R. Visser
This Submission thread is now published as
|Authors (as registered SciPost users):||Manus Visser|
|Preprint Link:||scipost_202303_00042v2 (pdf)|
|Date submitted:||2023-04-23 21:26|
|Submitted by:||Visser, Manus|
|Submitted to:||SciPost Physics|
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.
Published as SciPost Phys. 15, 023 (2023)
List of changes
We have replaced the opening of section 2.1 with text that addresses the issue of boundary conditions.
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