First-Order General-Relativistic Viscous Fluid Dynamics

We present the first generalization of Navier-Stokes theory to relativity that satisfies all following properties: (a) system coupled Einstein’s equations is causal and strongly hyperbolic; (b) equilibrium states are stable; (c) leading dissipative contributions present, i.e., shear viscosity, bulk thermal conductivity; (d) nonzero baryon number included; (e) entropy production non-negative in regime validity theory; (f) above hold nonlinear without any simplifying symmetry assumptions. These properties accomplished using a Eckart’s containing only hydrodynamic variables, so no new extended degrees freedom needed as Müller-Israel-Stewart theories. Property (b), particular, follows from more general result we also establish, namely, sufficient conditions when added stability fluid’s rest frame imply reference obtained via Lorentz transformation All our results mathematically rigorously established. The framework presented here provides starting point for systematic investigations general-relativistic viscous phenomena neutron star mergers.Received 9 October 2020Revised 18 January 2022Accepted 15 February 2022DOI:https://doi.org/10.1103/PhysRevX.12.021044Published by American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution this work must maintain attribution author(s) published article’s title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasFluids & classical fields curved spacetimeGeneral relativityGeneral solutionsTechniquesRelativistic hydrodynamicsGravitation, Cosmology AstrophysicsFluid Dynamics