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

Errata
  • Minor comments added v2, JHEP version; v3 corrected formulae and plot for heat capacity and fixed typo in Appendix A (original conclusions unaltered).
  • DOI : 10.1007/jhep04(2025)092
Published inThe journal of high energy physics, vol. 2022, no. 8, 75
Publication date2022
First online date2022-08-04
Abstract

We study the semi-classical thermodynamics of two-dimensional de Sitter space (dS$_{2}$) in Jackiw-Teitelboim (JT) gravity coupled to conformal matter. We extend the quasi-local formalism of Brown and York to 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 dS$_{2}$ backgrounds, without invoking the replica trick. We discuss the implications of our findings for static patch de Sitter holography.

Keywords
  • 2D Gravity
  • Gauge-Gravity Correspondence
  • Models of Quantum Gravity
  • Dimension: 2
  • Matter: conformal
  • Gravitation: coupling
  • Fluctuation: thermal
  • Charge: conservation law
  • Space: de Sitter
Citation (ISO format)
SVESKO, Andrew et al. Quasi-local energy and microcanonical entropy in two-dimensional nearly de Sitter gravity. In: The journal of high energy physics, 2022, vol. 2022, n° 8, p. 75. doi: 10.1007/jhep08(2022)075
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Erratum - Version 3
Identifiers
Additional URL for this publicationhttps://link.springer.com/10.1007/JHEP08(2022)075
Journal ISSN1029-8479
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