Surface tension with Normal Curvature in Curved Space-Time

TL;DR

This paper introduces a geometric approach to include surface tension in the boundary action of curved space-time, relating it to normal curvature and energy, and derives classical relations in weak fields.

Contribution

It provides a new geometric formulation of surface tension in curved space-time, linking it to normal curvature, energy, and boundary actions, extending classical relations.

Findings

Negative tangential pressure is independent of four-velocity.

Surface tension relates to normal curvature and energy of the surface layer.

Classical Kelvin's relation is derived in the weak field, static case.

Abstract

With an aim to include the contribution of surface tension in the action of the boundary, we define the tangential pressure in terms of surface tension and Normal curvature in a more naturally geometric way. First, we show that the negative tangential pressure is independent of the four-velocity of a very thin hyper-surface. Second, we relate the 3-pressure of a surface layer to the normal curvature and the surface tension. Third, we relate the surface tension to the energy of the surface layer. Four, we show that the delta like energy flows across the hyper-surface will be zero for such a representation of intrinsic 3-pressure. Five, for the weak field approximation and for static spherically symmetric configuration, we deduce the classical Kelvin's relation. Six, we write a modified action for the boundary having contributions both from surface tension and normal curvature of the surface layer. Also we propose a method to find the physical action assuming a reference background, where the background is not flat.