Abstract
We study SO(d + 1) invariant solutions of the classical vacuum Einstein equations in p + d + 3 dimensions. In the limit d → ∞ 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 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 determine the 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.
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Bhattacharyya, S., De, A., Minwalla, S. et al. A membrane paradigm at large D. J. High Energ. Phys. 2016, 76 (2016). https://doi.org/10.1007/JHEP04(2016)076
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DOI: https://doi.org/10.1007/JHEP04(2016)076