Causal, stable first-order viscous relativistic hydrodynamics with ideal gas microphysics

Abstract

We present the first numerical analysis of causal, stable first-order relativistic hydrodynamics with ideal gas microphysics, based in the formalism developed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK theory). The BDNK approach provides definitions for the conserved stress-energy tensor and baryon current, and rigorously proves causality, local well-posedness, strong hyperbolicity, and linear stability (about equilibrium) for the equations of motion, subject to a set of coupled nonlinear inequalities involving the undetermined model coefficients (the choice for which defines the ``hydrodynamic frame''). We present a class of hydrodynamic frames derived from the relativistic ideal gas ``gamma-law'' equation of state which satisfy the BDNK constraints, and explore the properties of the resulting model for a series of $(0+1)\mathrm{D}$ and $(1+1)\mathrm{D}$ tests in 4D Minkowski spacetime. These tests include a comparison of the dissipation mechanisms in Eckart, BDNK, and M\"uller-Israel-Stewart theories, as well as investigations of the impact of hydrodynamic frame on the causality and stability properties of Bjorken flow, planar shockwave, and heat flow solutions.