Systematic study of exact solutions in second-order conformal hydrodynamics

Abstract

In this paper we present the details of our previous work on exact solutions in second-order conformal hydrodynamics together with a number of new solutions found by mapping Minkowski space onto various curved spacetimes such as anti-de Sitter space and hyperbolic space. We analytically show how the solutions of ideal hydrodynamics are modified by the second-order effects including vorticity. We also find novel boost-invariant exact solutions which exist only in second-order hydrodynamics and have an unusual dependence on the proper time.

Hydrodynamic transport coefficients for the non-conformal quark-gluon plasma from holography

“…From (3.33) and (3.37), one obtains the famous ratio 38) which is actually valid for a broad class of gravity duals [68,69]. The second order hydrodynamic transport coefficients κ and τ π for the SYM plasma are found by substituting (3.35) into (3.3) and (3.4), respectively…”

“…Generalizing the previous analysis involving 2nd order terms in a conformal 5 Another way to understand how dissipation appears is to notice that, for instance, in this NS fluid the inclusion of πµν breaks the time reversal invariance present in the ideal fluid equations of motion. However, it is possible to find nontrivial fluid patterns involving second order gradients where πµν is nonzero but time reversal is not broken -see [37,38]. 6 Note that the mean free path for bulk viscosity is different than that for shear viscosity [39].…”

Non-boost-invariant solution of relativistic hydrodynamics in1+3dimensions

“…Yet, the transition from one-dimensional to three-dimensional expansions is expected on general grounds [1], and it is reassuring to see this analytically. It is remarkable that, although the two solutions (18) and (19) are trivially related by the reflection symmetry ρ ⊥ → −ρ ⊥ in dS 2 × H 2 (see Fig. 1), they appear quite distinct in Minkowski space.…”

“…Unfortunately, we have not found an exact analytical expression α(ρ ⊥ , η ⊥ ) which interpolates the limiting solutions (18), (19). We can however construct an approximate solution perturbatively in the formε…”

“…However, in ideal hydrodynamics (4) is not an independent equation and trivially solved by n ∝ T 3 . As demonstrated in [12,18,19], if the equation of state is relativistic ε = 3p, a powerful method to construct nontrivial solutions is available. Instead of working in Minkowski space with the metric…”