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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 demonstrate that this correspondence extends to all orders in a 1/D expansion and outline a systematic method for deriving the corrected membrane equation in a power series expansion in 1/D. As an illustration of our method we determine the first subleading corrections to the membrane equations of motion. A qualitatively new effect at this order is that the divergence of the membrane velocity is nonzero and proportional to the square of the shear tensor reminiscent of the entropy current of hydrodynamics. As a test, we use our modified membrane equations to compute the corrections to frequencies of light quasinormal modes about the Schwarzschild black hole and find a perfect match with earlier computations performed directly in the gravitational bulk.
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
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
We study the evolution of black hole collisions and ultraspinning black hole instabilities in higher dimensions. These processes can be efficiently solved numerically in an effective theory in the limit of large number of dimensions D. We present evi
It has recently been demonstrated that black hole dynamics in a large number of dimensions $D$ reduces to the dynamics of a codimension one membrane propagating in flat space. In this paper we define a stress tensor and charge current on this membran
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