4.7 Article

First-Order General-Relativistic Viscous Fluid Dynamics

Journal

PHYSICAL REVIEW X
Volume 12, Issue 2, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevX.12.021044

Keywords

-

Funding

  1. Sloan Research Fellowship
  2. Alfred P. Sloan foundation
  3. NSF [DMS-2107701]
  4. U.S. Department of Energy, Office of Science, Office for Nuclear Physics [DE-SC0021301]
  5. U.S. Department of Energy (DOE) [DE-SC0021301] Funding Source: U.S. Department of Energy (DOE)

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We present the first generalization of Navier-Stokes theory to relativity that satisfies multiple properties. These properties are accomplished using a generalization of Eckart's theory containing only the hydrodynamic variables.
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 M??ller-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.

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