A hadron resonance gas model including all known particles and resonances with masses m < 2 GeV and an exponentially rising density of Hagedorn states for m > 2 GeV is used to obtain an upper bound on the shear viscosity to entropy density ratio, eta/s approximately 1/(4pi), of hadronic matter near Tc. We found a large trace anomaly and small speed of sound near Tc, which agree well with recent lattice calculations. We comment on the bulk viscosity to entropy density ratio close to Tc.

A new approach is described to help improve the foundations of relativistic viscous fluid dynamics and its coupling to general relativity. Focusing on neutral conformal fluids constructed solely in terms of hydrodynamic variables, we derive the most general viscous energy-momentum tensor yielding equations of motion of second order in the derivatives, which is shown to provide a novel type of generalization of the relativistic Navier-Stokes equations for which causality holds. We show how this energy-momentum tensor may be derived from conformal kinetic theory. We rigorously prove existence, uniqueness, and causality of solutions of this theory (in the full nonlinear regime) both in a Minkowski background and also when the fluid is dynamically coupled to Einstein's equations. Linearized disturbances around equilibrium in Minkowski spacetime are stable in this causal theory. A numerical study reveals the presence of an out-of-equilibrium hydrodynamic attractor for a rapidly expanding fluid. Further properties are also studied and a brief discussion of how this approach can be generalized to non-conformal fluids is presented. 9 For geometric equations such as Einstein's equations, uniqueness is understood in a geometric sense, i.e., up to changes by diffeomorphisms. See, e.g., [11, Theorem 10.2.2]. 10 Strictly speaking, we are defining here local well-posedness of the initial value problem, which is the relevant notion of existence and uniqueness for evolution problems. We can also define local well-posedness for boundary value problems, etc. 11 In the mathematical literature, continuity with respect to the initial data is sometimes also referred to as stability, but we stress that this is entirely different from the notion of stability which is discussed in this paper (which follows the notion of stability introduced in [19], see section V). For example, the ordinary differential equationẋ = x, x(0) = x 0 has solution x(t) = x 0 e t , which varies continuously with x 0 . However, the trivial solution x trivial (t) ≡ 0 corresponding to x 0 = 0 is unstable in the terminology of this paper in that for any x 0 = 0, x(t) will diverge exponentially from x trivial .15 Provided the weak energy condition is satisfied, see section VIII B and Ref. [91]. 16 This meaning of the word frame has nothing to do with "rest" and "boosted frames." Unfortunately, these terminologies are too widespread to be changed here. Hence, we use the word frame to refer to both a choice of local temperature and velocity, e.g., the Landau frame, and in the usual sense of relativity, e.g., the rest frame. The difference between both uses will be clear from the context. We also note that frame, in the sense of a choice of local variables, has been used unevenly in the literature. In [92], for instance, frame is used in the same sense as employed here. In [23], the authors employ frame, or, more specifically, hydrodynamic frame, to refer solely to the choice that determines the local flow velocity, while the choices that determine the local temperatur...

We present an exact solution of the relativistic Boltzmann equation for a system undergoing boost-invariant longitudinal and azimuthally symmetric transverse flow ("Gubser flow"). The resulting exact non-equilibrium dynamics is compared to 1st-and 2nd-order relativistic hydrodynamic approximations for various shear viscosity to entropy density ratios. This novel solution can be used to test the validity and accuracy of different hydrodynamic approximations in conditions similar to those generated in relativistic heavy-ion collisions.

We present an exact solution to the Boltzmann equation which describes a system undergoing boost-invariant longitudinal and azimuthally symmetric radial expansion for arbitrary shear viscosity to entropy density ratio. This new solution is constructed by considering the conformal map between Minkowski space and the direct product of three dimensional de Sitter space with a line.The resulting solution respects SO(3) q ⊗ SO(1, 1) ⊗ Z 2 symmetry. We compare the exact kinetic solution with exact solutions of the corresponding macroscopic equations that were obtained from the kinetic theory in ideal and second-order viscous hydrodynamic approximations. The macroscopic solutions are obtained in de Sitter space and are subject to the same symmetries used to obtain the exact kinetic solution.

Bulk viscosity effects on the collective flow harmonics in heavy ion collisions are investigated, on an event by event basis, using a newly developed 2+1 Lagrangian hydrodynamic code named v-USPhydro which implements the Smoothed Particle Hydrodynamics (SPH) algorithm for viscous hydrodynamics. A new formula for the bulk viscous corrections present in the distribution function at freeze-out is derived starting from the Boltzmann equation for multi-hadron species. Bulk viscosity is shown to enhance the collective flow Fourier coefficients from v2(pT ) to v5(pT ) when pT ∼ 1 − 3 GeV even when the bulk viscosity to entropy density ratio, ζ/s, is significantly smaller than 1/(4π).