Comparison between fluid-gravity and membrane-gravity dualities for Einstein-Maxwell system

TL;DR

This paper compares two perturbation techniques, derivative expansion and large-D expansion, for generating black-brane solutions in Einstein-Maxwell systems, establishing their equivalence in a specific parameter regime.

Contribution

It demonstrates the equivalence of fluid-gravity and membrane-gravity dualities for Einstein-Maxwell systems up to first non-trivial order, extending previous non-charged results.

Findings

Established the equivalence of the two perturbation techniques.

Mapped dynamical black-brane geometry to AdS space at finite dimensions.

Generalized earlier non-charged system results to Einstein-Maxwell systems.

Abstract

Derivative expansion and large-$D$ expansion are two perturbation techniques, which are used to generate dynamical black-brane solutions to Einstein's equations in presence of negative cosmological constant. In this note we have compared these two techniques and established the equivalence of the gravity solutions generated by these two different techniques in appropriate regime of parameter space up to first non-trivial order in both the perturbation parameters for Einstein-Maxwell systems, generalizing the earlier works of [arXiv:1807.05058], [arXiv:1902.00854] for non-charged systems. An one-to-one map between dynamical black-brane geometry and AdS space, which also exists at finite number of dimensions, has also been established.