Is first-order relativistic hydrodynamics in general frame stable and causal for arbitrary interaction?

Abstract

We derive a first-order, stable and causal, relativistic hydrodynamic theory from the microscopic kinetic equation using the gradient expansion technique in a general frame. The general frame is introduced from the arbitrary matching conditions for hydrodynamic fields. The interaction is introduced in the relativistic Boltzmann equation through momentum-dependent relaxation time approximation (MDRTA). We demonstrate here for the first time that not only the general frame choice but also the momentum dependence of microscopic interaction rate, captured through MDRTA, is imperative for producing the essential field corrections that give rise to a causal and stable first-order theory.

Perturbative approaches in relativistic kinetic theory and the emergence of first-order hydrodynamics

“…In Section IV B we derived the fluid-dynamical equations that emerge from the first order truncation of the Hilbert expansion. We found that the equilibrium fields n 0 , ε 0 , and u µ satisfy the relativistic Euler equation ( 66), while the dissipative currents obey the linear differential equations (72), with the constrains given by Eqs. (76).…”

“…As mentioned above, the first derivation of BDNK theory from kinetic theory was done in the original works [33,35]. After that, other approaches were pursued in [71,72]. Reference [71] discussed how BDNK may be derived from holography, using the fluid/gravity correspondence [73].…”

“…They also provided a derivation of BDNK from kinetic theory using ideas from the Hilbert series. Reference [72] focused on the effects of a momentum-dependent relaxation time coefficient on the calculation of transport coefficients.…”