Causality and existence of solutions of relativistic viscous fluid dynamics with gravity

TL;DR

This paper develops a new, causal relativistic viscous fluid theory coupled with gravity, proving existence and stability of solutions, and demonstrating novel hydrodynamic behaviors through numerical analysis.

Contribution

It introduces a second-order, causal energy-momentum tensor for conformal fluids and establishes its mathematical well-posedness and physical stability.

Findings

The theory ensures causality and well-posedness of solutions.

Existence and uniqueness are proven in both Minkowski and gravitationally coupled scenarios.

Numerical simulations reveal an out-of-equilibrium hydrodynamic attractor.

Abstract

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.