2023/07/26 by Aydın Tavlayan, Bayram Tekin, Tavlayan, Aydin +1 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2307.14210
openalex publication_date 2023/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, [Phys. Rev. Lett. 130, 221501 (2023)] Jacobson and Visser calculated the quantum partition function of a fixed, finite volume of a region with the topology of a ball in the saddle point approximation within the context of Einstein's gravity with or without a cosmological constant. The result can be interpreted as the dimension of Hilbert space of the theory. Here we extend their computation to a theory defined in principle with infinitely many powers of curvature in three dimensions. We confirm their result: The partition function of a spatial region in the leading saddle point approximation is given as the exponential of the Bekenstein-Hawking or the Wald entropy of the boundary of the finite spatial region both in the case of zero and finite cosmological constant. In the latter case, the effective Newton's constant appears in the entropy formula. The calculations lend support to the holographic nature of gravity for finite regions of space with a boundary.