Fluid-gravity and membrane-gravity dualities. Comparison at subleading orders

Abstract

Abstract In this note, we have compared two different perturbation techniques that could be used to generate solutions of Einstein’s equations in the presence of negative cosmological constant. One of these two methods is derivative expansion and the other is an expansion in inverse powers of dimension. Both the techniques generate space-time with a singularity shielded by a dynamical event horizon. We have shown that in the appropriate regime of parameter space and with an appropriate choice of coordinates, the metrics and corresponding horizon dynamics, generated by these two different techniques, are exactly equal to the order the solutions are known both sides. This work is essentially an extension of [1] where the authors have shown the equivalence of the two techniques up to the first non-trivial order.

Keywords

• Black Holes
• Classical Theories of Gravity