Path Integrals for Causal Diamonds and the Covariant Entropy Principle

Patrick Draper; Szilard Farkas; Tom Banks

Path Integrals for Causal Diamonds and the Covariant Entropy Principle

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arxiv 2008.03449 v1 pith:OWPFVD37 submitted 2020-08-08 hep-th gr-qc

Tom Banks , Patrick Draper , Szilard Farkas This is my paper · ORCID

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keywords diamondcausaldiamondseuclideanaroundboundaryentropypunctures

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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.

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Hilbert Bundles and Holographic Space-time: the Hydrodynamic Approach to Gravity
hep-th 2025-02 conditional novelty 3.0 of 10

Einstein's equations are treated as hydrodynamic equations for the area-law entropy of causal diamonds, with quantum dynamics proposed to live in a Hilbert bundle over spacetime geodesics.

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