# Nonlinear causality of general first-order relativistic viscous hydrodynamics

## TL;DR

This paper derives a causal, stable, and unique first-order relativistic viscous hydrodynamics theory without extended variables, applicable in full nonlinear regimes and supported by a kinetic theory model.

## Contribution

It introduces a novel first-order energy-momentum tensor ensuring causality and stability, with rigorous proofs of existence and uniqueness of solutions in general settings.

## Key findings

- The theory is causal if out-of-equilibrium energy density and heat flow are nonzero.
- Conditions for linear stability around equilibrium are established.
- Mathematically rigorous proofs of local existence and uniqueness are provided.

## Abstract

Effective theory arguments are used to derive the most general energy-momentum tensor of a relativistic viscous fluid with an arbitrary equation of state (in the absence of other conserved currents) that is first-order in the derivatives of the energy density and flow velocity and does not include extended variables such as in Mueller-Israel-Stewart-like theories. This energy-momentum tensor leads to a causal theory, provided one abandons the usual conventions for the out-of-equilibrium hydrodynamic variables put forward by Landau-Lifshitz and Eckart. In particular, causality requires nonzero out-of-equilibrium energy density corrections and heat flow. Conditions are found to ensure linear stability around equilibrium in flat space-time. We also prove local existence and uniqueness of solutions to the equations of motion. Our causality, existence, and uniqueness results hold in the full nonlinear regime, without symmetry assumptions, in four space-time dimensions, with or without coupling to Einstein's equations, and are mathematically rigorously established. Furthermore, a kinetic theory realization of this energy-momentum tensor is also provided.