Non-equilibrium thermodynamics of gravitational screens

TL;DR

This paper establishes a thermodynamic analogy for gravitational screens in Einstein gravity, showing they behave like viscous bubbles with surface tension, and links gravitational dynamics to non-equilibrium thermodynamics including entropy production and black-hole thermodynamics.

Contribution

It introduces a novel framework mapping Einstein gravity equations on a timelike surface to non-equilibrium thermodynamic equations of viscous bubbles, including surface tension effects.

Findings

Gravitational screens behave like viscous bubbles with surface tension.

Einstein equations correspond to thermodynamic equations like the first law and Young-Laplace.

Entropy production in gravity maps to gravitational wave production.

Abstract

We study the Einstein gravity equations projected on a timelike surface, which represents the time evolution of what we call a gravitational screen. We show that such a screen behaves like a viscous bubble with a surface tension and an internal energy, and that the Einstein equations take the same forms as non-equilibrium thermodynamic equations for a viscous bubble. We provide a consistent dictionary between gravitational and thermodynamical variables. In the non-viscous cases there are three thermodynamic equations which characterize a bubble dynamics: These are the first law, the Marangoni flow equation and the Young-Laplace equation. In all three equations the surface tension plays a central role: In the first law it appears as a work term per unit area, in the Marangoni flow its gradient drives a force, and in the Young-Laplace equation it contributes to a pressure proportional to the surface curvature. The gravity equations appear as a natural generalization of these bubble equations when the bubble itself is viscous and dynamical. In particular, it shows that the mechanism of entropy production for the viscous bubble is mapped onto the production of gravitational waves. We also review the relationship between surface tension and temperature, and discuss black-hole thermodynamics.