Shearing black holes and scans of the quark matter phase diagram

Abstract

Future facilities such as FAIR and NICA are expected to produce collisions of heavy ions generating quark-gluon plasmas with large values of the quark chemical potential; peripheral collisions in such experiments will also lead to large values of the angular momentum density, associated with the internal shearing motion of the plasma. It is well known that shearing motions in fluids can lead to instabilities which cause a transition from laminar to turbulent flow, and such instabilities in the QGP have recently attracted some attention. We set up a holographic model of this situation by constructing a gravitational dual system exhibiting an instability which is indeed triggered by shearing angular momentum in the bulk. We show that holography indicates that the transition to an unstable fluid happens more quickly as one scans across the quark matter phase diagram towards large values of the chemical potential. This may have negative consequences for the observability of quark polarization effects.

Gravity and on-shell probe actions

“…Related and extremely instructive results using probe branes in holographic set-ups have also appeared in the earlier literature [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

“…33 Of course, a is just a scale and we could set a = 1, but we find it convenient to keep a explicitly.…”

Holography of Little Inflation

“…It proves to be very stringent: the range μ B /T ≈ 1-100 discussed in [14] is greatly narrowed to ≈1 ≤ μ B /T ≤ ≈2. 35. Since the value of μ B /T at the quark matter critical point provides the lower bound around 1, this result means that, if the cosmic plasma does indeed undergo a first-order phase transition at the end of the plasma era, it must pass close to the critical point.…”

“…(See [31,35] for the details.) Notice that the (conformal) metric at infinity for this spacetime is represented by the metric −dt 2 + L 2 dψ 2 + dζ 2 on S t in our earlier discussion.…”

“…Furthermore, we are ignoring the effects of cosmic vorticity: that is the customary assumption (though it might be desirable under some circumstances to reconsider it [54]); but, again, the analogous assumption, that the angular momentum density is negligible, is certainly not normally justified in the heavy-ion case, where the holographic dual is a black hole endowed with angular momentum, as in [55,35,56,57]. Again, as we have seen, the time evolution of all physical parameters in the cosmic case is controlled in a simple way by a single function, a(t); but it is not clear that any such simple description of the dynamics is possible for a heavy-ion plasma.…”