2025/07/30 by Kwinten Fransen, Temple He, Fransen, Kwinten +3 · 2 citations
Physics and Astronomy · #Cosmology and Gravitation Theories #Quantum Electrodynamics and Casimir Effect #Advanced Mathematical Theories and Applications
paper · pdf · doi:10.48550/arxiv.2507.22977
We compute a gravitational on-shell action of a finite, spherically symmetric causal diamond in (d+2)-dimensional Minkowski spacetime, finding it is proportional to the area of the bifurcate horizon AB. We then identify the on-shell action with the saddle point of the Euclidean gravitational path integral, which is naturally interpreted as a partition function. This partition function is thermal with respect to a modular Hamiltonian K. Consequently, we determine, from the on-shell action using standard thermodynamic identities, both the mean and variance of the modular Hamiltonian, finding ⟨ K ⟩ = ⟨ (ΔK)2 ⟩ = \fracAB4 GN. Finally, we show that modular fluctuations give rise to fluctuations in the geometry, and compute the associated phase shift of massless particles traversing the diamond under such fluctuations.