Surface Layers in General Relativity and Their Relation to Surface Tensions

TL;DR

This paper explores the analogy between surface tension and intrinsic pressure in thin shells within general relativity, deriving relations that connect classical surface tension concepts with relativistic surface layers.

Contribution

It establishes a relativistic analogue to Kelvin's relation and demonstrates how surface tension can be represented by intrinsic 3-pressure in thin shells.

Findings

Intrinsic 3-pressure is analogous to negative surface tension.

Surface layers with no gravitational mass can be matched in Schwarzschild solutions.

Relativistic Kelvin's relation is derived from the equation of motion.

Abstract

For a thin shell, the intrinsic 3-pressure will be shown to be analogous to -A, where A is the classical surface tension: First, interior and exterior Schwarzschild solutions will be matched together such that the surface layer generated at the common boundary has no gravitational mass; then its intrinsic 3-pressure represents a surface tension fulfilling Kelvin's relation between mean curvature and pressure difference in the Newtonian limit. Second, after a suitable definition of mean curvature, the general relativistic analogue to Kelvin's relation will be proven to be contained in the equation of motion of the surface layer.