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

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 paper 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 [1, 2] for noncharged 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.

Black Rings in Large $D$ Membrane Paradigm at the First Order

“…While the other branch, known as the "large D membrane paradigm" [53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69] states that the dynamical black holes in large D have one-to-one correspondence to the dynamics of a codimension one hypersurface, called a "membrane", which doesn't backreact on its background. In this nongravitational dual, the membrane dynamics is governed by what are called the "membrane equations of motion", and the dynamical data associated with the membrane completely defines the corresponding black hole solution.…”