First-Order General-Relativistic Viscous Fluid Dynamics

Fábio S. Bemfica, Marcelo M. Disconzi, Jorge Noronha

Research output: Contribution to journalArticlepeer-review


We present the first generalization of Navier-Stokes theory to relativity that satisfies all of the following properties: (a) the system coupled to Einstein's equations is causal and strongly hyperbolic; (b) equilibrium states are stable; (c) all leading dissipative contributions are present, i.e., shear viscosity, bulk viscosity, and thermal conductivity; (d) nonzero baryon number is included; (e) entropy production is non-negative in the regime of validity of the theory; (f) all of the above hold in the nonlinear regime without any simplifying symmetry assumptions. These properties are accomplished using a generalization of Eckart's theory containing only the hydrodynamic variables, so that no new extended degrees of freedom are needed as in Müller-Israel-Stewart theories. Property (b), in particular, follows from a more general result that we also establish, namely, sufficient conditions that when added to stability in the fluid's rest frame imply stability in any reference frame obtained via a Lorentz transformation All of our results are mathematically rigorously established. The framework presented here provides the starting point for systematic investigations of general-relativistic viscous phenomena in neutron star mergers.

Original languageEnglish (US)
Article number021044
JournalPhysical Review X
Issue number2
StatePublished - Jun 2022

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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