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We study $SO(d+1)$ invariant solutions of the classical vacuum Einstein equations in $p+d+3$ dimensions. In the limit $d to infty$ with $p$ held fixed we construct a class of solutions labelled by the shape of a membrane (the event horizon), together with a `velocity field that lives on this membrane. We demonstrate that our metrics can be corrected to nonsingular solutions at first sub-leading order in $frac{1}{d}$ if and only if the membrane shape and `velocity field obey equations of motion which we determine. These equations define a well posed initial value problem for the membrane shape and this `velocity and so completely determinethe dynamics of the black hole. They may be viewed as governing the non-linear dynamics of the light quasi normal modes of Emparan, Suzuki and Tanabe.
In the large D limit, and under certain circumstances, it has recently been demonstrated that black hole dynamics in asymptotically flat spacetime reduces to the dynamics of a non gravitational membrane propagating in flat D dimensional spacetime. We
We find the equations of motion of membranes dual to the black holes in Einstein-Gauss-Bonnet (EGB) gravity to leading order in 1/D in the large D regime. We also find the metric solutions to the EGB equations to first subleading order in 1/D in term
The membrane paradigm posits that black hole microstates are dynamical degrees of freedom associated with a physical membrane vanishingly close to the black holes event horizon. The soft hair paradigm postulates that black holes can be equipped with
It has recently been demonstrated that black hole dynamics at large D is dual to the motion of a probe membrane propagating in the background of a spacetime that solves Einsteins equations. The equation of motion of this membrane is determined by the
We show that at the level of linear response the low frequency limit of a strongly coupled field theory at finite temperature is determined by the horizon geometry of its gravity dual, i.e. by the membrane paradigm fluid of classical black hole mecha