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

TL;DR

This paper introduces a numerically analyzed, causal, and stable first-order relativistic hydrodynamics framework based on BDNK theory, incorporating ideal gas microphysics, and explores its properties through various tests in Minkowski spacetime.

Contribution

It provides the first numerical implementation and analysis of BDNK-based first-order relativistic hydrodynamics with ideal gas microphysics, demonstrating causality, stability, and physical consistency.

Findings

BDNK theory ensures causality and stability under certain conditions.

Hydrodynamic frame choice significantly affects flow properties.

Comparison shows differences in dissipation mechanisms across theories.

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)D and (1+1)D tests in 4D Minkowski spacetime. These tests include a comparison of the dissipation mechanisms in Eckart, BDNK, and Muller-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.