Generalized planar black holes and the holography of hydrodynamic shear

AdS black holes with planar event horizon topology play a central role in AdS/CFT holography, and particularly in its applications. Generalizations of the known planar black holes can be found by considering the Plebański–Demiański metrics, a very general family of exactly specified solutions of the Einstein equations. These generalized planar black holes may be useful in applications. We give a concrete example of this in the context of the holographic description of the Quark–Gluon Plasma (QGP). We argue that our generalized planar black holes allow us to construct a model of the internal shearing motion generated when the QGP is produced in peripheral heavy-ion collisions. When embedded in string theory, the bulk physics is in fact unstable. We find however that this instability may develop too slowly to affect the evolution of the plasma, except possibly for high values of the quark chemical potential, such as will be studied in experimental scans of the quark matter phase diagram.