Large D gravity and charged membrane dynamics with nonzero cosmological constant

TL;DR

This paper derives charged black hole solutions and membrane dynamics in Einstein-Maxwell theory with a cosmological constant in large D dimensions, revealing dual membrane behavior and stability properties.

Contribution

It introduces a new class of charged black hole solutions and membrane equations in large D Einstein-Maxwell systems with cosmological constant, extending previous work to include charge and cosmological backgrounds.

Findings

Derived charged black hole solutions in large D with cosmological constant.

Formulated membrane equations governing charged membrane dynamics.

Validated membrane equations via quasi-normal mode analysis.

Abstract

In this paper, we have found a class of dynamical charged 'black-hole' solutions to Einstein-Maxwell system with a non-zero cosmological constant in a large number of spacetime dimensions. We have solved up to the first sub-leading order using large D scheme where the inverse of the number of dimensions serves as the perturbation parameter. The system is dual to a dynamical membrane with a charge and a velocity field, living on it. The dual membrane has to be embedded in a background geometry that itself, satisfies the pure gravity equation in presence of a cosmological constant. Pure AdS / dS are particular examples of such background. We have also obtained the membrane equations governing the dynamics of the charged membrane. The consistency of our membrane equations is checked by calculating the quasi-normal modes with different Einstein-Maxwell systems in AdS/dS.