Abstract
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.
- Received 9 October 2020
- Revised 18 January 2022
- Accepted 15 February 2022
DOI:https://doi.org/10.1103/PhysRevX.12.021044
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
General relativity predicts that a system that is out of thermal equilibrium evolves through spacetime differently than when it is in equilibrium. The recent detection of gravitational waves produced by neutron star mergers provides the first way to test this universal prediction of general relativity as the ultradense matter formed in these violent collisions moves away from thermal equilibrium before it meets its fate (for instance, the formation of a black hole). However, despite many attempts dating back to seminal work in 1940, a consistent description of dissipative phenomena in strong gravitational fields is still lacking. We propose a definite solution to this 82-year-old open question in physics and mathematics.
Our new approach uses well-known physical principles, such as causality and the second law of thermodynamics, and solid mathematics to redefine the state of the art of the field of relativistic fluid dynamics. The synergistic combination of physics and mathematics in this work establishes, for the first time, a common unifying framework that can be directly used in numerical simulations of the ultradense viscous matter formed in neutron star mergers.
Next steps involve using this formalism to perform detailed numerical simulations of neutron star mergers and of high-density, relativistic, heavy-ion collisions.
