– Europe/Lisbon
Room P3.10, Mathematics Building — Online
Quasi-local energy and microcanonical entropy in two-dimensional nearly de Sitter gravity
We study the semi-classical thermodynamics of two-dimensional de Sitter space ($\operatorname{dS}_2$) in Jackiw-Teitelboim (JT) gravity coupled to conformal matter. We extend the quasi-local formalism of Brown and York to $\operatorname{dS}_2$, 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 $\operatorname{dS}_2$ backgrounds, without invoking the replica trick. We discuss the implications of our findings for static patch de Sitter holography.