Relativistic Elasticity of Stationary Fluid Branes

TL;DR

This paper demonstrates that stationary fluid configurations on dynamical surfaces can behave like elastic branes under small deformations, revealing an elastic character of black branes in a gravitational context.

Contribution

It establishes a connection between fluid dynamics on dynamical surfaces and elastic behavior of branes, independent of space-time dimensions and gravitational duals.

Findings

Stationary fluid configurations can behave as elastic branes under small deformations.

Black branes exhibit elastic properties when subjected to extrinsic perturbations.

Results are applicable across various space-time dimensions and gravitational duals.

Abstract

Fluid mechanics can be formulated on dynamical surfaces of arbitrary co-dimension embedded in a background space-time. This has been the main object of study of the blackfold approach in which the emphasis has primarily been on stationary fluid configurations. Motivated by this approach we show under certain conditions that a given stationary fluid configuration living on a dynamical surface of vanishing thickness and satisfying locally the first law of thermodynamics will behave like an elastic brane when the surface is subject to small deformations. These results, which are independent of the number of space-time dimensions and of the fluid arising from a gravitational dual, reveal the (electro)elastic character of (charged) black branes when considering extrinsic perturbations.