Non-equilibrium thermodynamics of gravitational screens

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.

30 pages, 3 figures. This is the published version in Classical and Quantum Gravity. Typos are modified, references are added, discussions (especially, of section 6) are clarified but the main results do not change

References in corpus (10)

• Nonlinear Fluid Dynamics from Gravity
• Local Fluid Dynamical Entropy from Gravity
• Minimal conditions for the existence of a Hawking-like flux
• Entropy density of spacetime and the Navier-Stokes fluid dynamics of null surfaces
• A generalized Damour-Navier-Stokes equation applied to trapping horizons
• New theoretical approaches to black holes
• Area evolution, bulk viscosity and entropy principles for dynamical horizons
• Phenomenological Description of the Interior of the Schwarzschild Black Hole
• Gravitational Energy, Local Holography and Non-equilibrium Thermodynamics
• A Young-Laplace law for black hole horizons

Cited by in corpus (12)

• Null Conservation Laws for Gravity
• Bubble Networks: Framed Discrete Geometry for Quantum Gravity
• Quantum Surface and Intertwiner Dynamics in Loop Quantum Gravity
• Quantum gravity at the corner
• Motion of localized sources in general relativity: gravitational self-force from quasilocal conservation laws
• The thermodynamics of quantum spacetime histories
• Towards self dual Loop Quantum Gravity
• Quasilocal energy and thermodynamic equilibrium conditions
• Bulk entropy is crucial to validate the second law of the extended black hole thermodynamics
• Energy of cosmological spacetimes and perturbations: a quasilocal approach
• Entropy theorems in classical mechanics, general relativity, and the gravitational two-body problem
• Large Gauge Symmetries of an Asymptotically de Sitter Horizon: An Extended First Law of Thermodynamics