Disrupting Entanglement of Black Holes

We study entanglement in thermofield double states of strongly coupled CFTs by analyzing two-sided Reissner-Nordström solutions in AdS. The central object of study is the mutual information between a pair of regions, one on each asymptotic boundary of the black hole. For large regions the mutual information is positive and for small ones it vanishes; we compute the critical length scale, which goes to infinity for extremal black holes, of the transition. We also generalize the butterfly effect of Shenker and Stanford [1] to a wide class of charged black holes, showing that mutual information is disrupted upon perturbing the system and waiting for a time of order logE/δE in units of the temperature. We conjecture that the parametric form of this timescale is universal. email: [email protected] ar X iv :1 40 5. 73 65 v2 [ he pth ] 2 3 Ju n 20 14