Deformed AdS4-Reissner-Nordstr\"om black branes and shear viscosity-to-entropy density ratio

A family of deformed AdS4-Reissner-Nordstr"om 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 AdS4-Reissner-Nordstr"om 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 tidal charge.