Deformed AdS$$_4$$ 4 –Reissner–Nordström black branes and shear viscosity-to-entropy density ratio

Abstract

Abstract A family of deformed AdS$$_4$$ 4 –Reissner–Nordström black branes, governed by a free parameter, is derived using the ADM formalism, in the context of the membrane paradigm. Their new event horizons, the Hawking temperature and other aspects are scrutinized. AdS/CFT near-horizon methods are then implemented to compute the shear viscosity-to-entropy ratio for the deformed AdS$$_4$$ 4 –Reissner–Nordström metric. The Killing equation is shown to yield new values for the free parameter and the shear viscosity-to-entropy ratio is used to derive a reliable range for the tidal charge.