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arXiv · 2203.00700

Quasi-local energy and microcanonical entropy in two-dimensional nearly de Sitter gravity

Andrew Svesko·Evita Verheijden·Erik P. Verlinde·Manus R. Visser
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Abstract

We study the semi-classical thermodynamics of two-dimensional de Sitter space ($\text{dS}_{2}$) in Jackiw-Teitelboim (JT) gravity coupled to conformal matter. We extend the quasi-local formalism of Brown and York to $\text{dS}_{2}$, where a timelike boundary is introduced in the static patch to uniquely define conserved charges, including quasi-local energy. The boundary divides the static patch into two systems, a cosmological system and a black hole system, the former being unstable under thermal fluctuations while the latter is stable. A semi-classical quasi-local first law is derived, where the Gibbons--Hawking entropy is replaced by the generalized entropy. In the microcanonical ensemble the generalized entropy is stationary. Further, we show the on-shell Euclidean microcanonical action of a causal diamond in semi-classical JT gravity equals minus the generalized entropy of the diamond, hence extremization of the entropy follows from minimizing the action. Thus, we provide a first principles derivation of the island rule for $U(1)$ symmetric $\text{dS}_{2}$ backgrounds, without invoking the replica trick. We discuss the implications of our findings for static patch de Sitter holography.

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Andrew Svesko, Evita Verheijden, Erik P. Verlinde, Manus R. Visser. 2025-03-21. Quasi-local energy and microcanonical entropy in two-dimensional nearly de Sitter gravity. https://doi.org/10.1007/jhep08(2022)075

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