What is a Gravitational Path Integral? {\it or} Gravitational Path Integrals as Fluctuating Gravito-Hydrodynamics

TL;DR

This paper derives gravitational path integral formulas from hydrodynamic assumptions linking spacetime geometry, entropy, and modular Hamiltonian fluctuations, impacting quantum gravity models and topology summation.

Contribution

It introduces a hydrodynamic framework explaining gravitational path integrals based on coarse-grained assumptions about spacetime and entropy relations.

Findings

Path integrals follow from hydrodynamic assumptions.

Implications for quantum gravity models.

Insights into topology summation in gravity.

Abstract

We show how Gravitational Path Integral formulae for various quantities that have been computed in the literature, follow from a few coarse grained hydrodynamic assumptions about the relations between space-time geometry, entropy, and fluctuations of the modular Hamiltonian of causal diamonds. These remarks have implications for the way we think about such path integrals in relation to a more fundamental model of quantum gravity, and to questions about which space-time topologies are actually summed over in real models.