Abstract
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.
Highlights
Collisions of heavy ions [1] are believed to produce a state of matter known as the QuarkGluon Plasma or Quark-Gluon Plasma (QGP)
One theoretical approach to understanding this state is based on holography, in which the QGP is modelled by a field theory dual to a gravitational system, a thermal AdS black hole [2,3,4,5]
The shearing motion of a fluid is described by a velocity profile, an expression of the velocity v(x) as a function of transverse distance from some axis. (In the case of plasma generated by heavy-ion collisions, it is customary to choose the axis to be that of the collision, that is, the axis along which the velocity vanishes; it is conventional to take it to be the z-axis.) This function is of basic importance, since it describes the internal dynamics of the plasma
Summary
Collisions of heavy ions [1] are believed to produce a state of matter known as the QuarkGluon Plasma or QGP. Some aspects of fluid behaviour depend only on the general shape of the profile, not on the details; these aspects, can be discussed in the QGP case, even in the absence of a precisely specified v(x) function Most important among these is the question as to whether the shearing motion described by v(x) is stable, in the hydrodynamic sense. In a recently proposed theoretical model of the shearing QGP (see [30,31] and references therein), it is suggested that the velocity profile does take a form satisfying the conditions of Fjørtoft’s theorem, and simulations of the consequent Kelvin–Helmholtz instability are generated This may well lead to observable effects, and so one obtains, in principle, a way of testing the model. Under these conditions, the plasma will behave in a manner quite different from predictions based on a simple Kelvin–Helmholtz effect
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