We test the cosmic censorship conjecture for a class of polarized AdS black branes (holes) in the Einstein-Maxwell theory at large number of dimensions D. We first derive a new set of effective equations describing the dynamics of the polarized black branes (holes) to leading order in the 1/D expansion. In the case of black branes, we construct ‘mushroom-type’ static solutions from the effective equations, where a spherical horizon is connected with an asymptotic planar horizon through a ‘neck’ which is locally black-string shape. We argue that this neck part (of black string) cannot be pinched off dynamically from the perspective of thermodynamical stability. In the case of black holes, we show that the equatorial plane on the spherical horizon cannot be sufficiently squashed unless the specific heat is positive. We also discuss that the solutions are stable against linear perturbation, agreeing with the thermodynamical argument. These results suggest that Gregory-Laflamme type instability does not occur at the neck, in favor of the cosmic censorship.
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