Path Integrals for Causal Diamonds and the Covariant Entropy Principle

Abstract

We study causal diamonds in Minkowski, Schwarzschild, (anti) de Sitter, and Schwarzschild-de Sitter spacetimes using Euclidean methods. The null boundaries of causal diamonds are shown to map to isolated punctures in the Euclidean continuation of the parent manifold. Boundary terms around these punctures decrease the Euclidean action by $A_{\diamond }/4$, where $A_{\diamond }$ is the area of the holographic screen around the diamond. We identify these boundary contributions with the maximal entropy of gravitational degrees of freedom associated with the diamond.

25 pages

References in corpus (4)

• Towards a derivation of holographic entanglement entropy
• JT gravity as a matrix integral
• Towards a quantum theory of de Sitter space
• Holographic Tensor Networks in Full AdS/CFT

Cited by in corpus (10)

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• Conformal Description of Near-Horizon Vacuum States
• Microcanonical Action and the Entropy of Hawking Radiation
• Euclidean de Sitter Black Holes and Microcanonical Equilibrium
• Entropy of causal diamond ensembles
• Quantum theory of three-dimensional de Sitter space
• Thermodynamics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime
• de Sitter Black Holes as Constrained States in the Euclidean Path Integral
• JT de Sitter Gravity as a Model of Coleman-de Luccia Tunneling
• Entropy and Black Holes in the Very Early Universe