Electroelasticity of Charged Black Branes

TL;DR

This paper develops a first-order corrected effective theory for charged black branes, revealing their electroelastic properties and deriving explicit solutions in string theory contexts, connecting gravity with classical electroelasticity.

Contribution

It introduces the first-order corrected dynamics of charged fluid branes, characterizes their electroelastic response, and constructs explicit black brane solutions in string theory demonstrating these properties.

Findings

Charged black branes exhibit electroelastic behavior described by Young modulus and piezoelectric moduli.

Explicit solutions for strained charged black branes are constructed in Einstein-Maxwell-dilaton gravity.

The electroelastic response coefficients are parameterized by four key response parameters.

Abstract

We present the first-order corrected dynamics of fluid branes carrying higher-form charge by obtaining the general form of their equations of motion to pole-dipole order. Assuming linear response theory, we characterize the corresponding effective theory of stationary bent charged (an)isotropic fluid branes in terms of two sets of response coefficients, the Young modulus and the piezoelectric moduli. We subsequently find large classes of examples in gravity of this effective theory, by constructing stationary strained charged black brane solutions to first order in a derivative expansion. Using solution generating techniques and bent neutral black branes as a seed solution, we obtain a class of charged black brane geometries carrying smeared Maxwell charge in Einstein-Maxwell-dilaton gravity. In the specific case of ten-dimensional space-time we furthermore use T-duality to generate bent black branes with higher-form charge, including smeared D-branes of type II string theory. By subsequently measuring the bending moment and the electric dipole moment which these geometries acquire due to the strain, we uncover that their form is captured by classical electroelasticity theory. In particular, we find that the Young modulus and the piezoelectric moduli of our strained charged black brane solutions are parameterized by a total of 4 response coefficients, both for the isotropic as well as anisotropic cases.