Surface Motions and Fluid Dynamics

TL;DR

This paper establishes a surprising equivalence between certain relativistic surface motions, including membrane dynamics, and steady-state irrotational inviscid fluid flow, revealing deep connections between geometry, fluid dynamics, and field theories.

Contribution

It demonstrates the equivalence between specific surface motions and fluid dynamics, and links SU(∞) Nahm equations to harmonic functions governing surface evolution.

Findings

Relativistic membrane motions correspond to steady-state fluid flows.

SU(∞) Nahm equations relate to harmonic functions in surface motion.

Scalar field theory linearizes under these conditions.

Abstract

A certain class of surface motions, including those of a relativistic membrane minimizing the 3-dimensional volume swept out in Minkowski-space, is shown to be equivalent to 3-dimensional steady-state irrotational inviscid isentropic gas-dynamics. The SU($\infty $) Nahm equations turn out to correspond to motions where the time $t$ at which the surface moves through the point $\ssatop\rhup{r}$ is a harmonic function of the three space-coordinates. This solution also implies the linearisation of a non-trivial-looking scalar field theory.