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Published December 15, 2022 | Published
Journal Article Open

Causal, stable first-order viscous relativistic hydrodynamics with ideal gas microphysics

Abstract

We present the first numerical analysis of causal, stable first-order relativistic hydrodynamics with ideal gas microphysics, based in the formalism developed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK theory). The BDNK approach provides definitions for the conserved stress-energy tensor and baryon current, and rigorously proves causality, local well-posedness, strong hyperbolicity, and linear stability (about equilibrium) for the equations of motion, subject to a set of coupled nonlinear inequalities involving the undetermined model coefficients (the choice for which defines the "hydrodynamic frame"). We present a class of hydrodynamic frames derived from the relativistic ideal gas "gamma-law" equation of state which satisfy the BDNK constraints, and explore the properties of the resulting model for a series of ( 0 + 1 ) D and ( 1 + 1 ) D tests in 4D Minkowski spacetime. These tests include a comparison of the dissipation mechanisms in Eckart, BDNK, and Müller-Israel-Stewart theories, as well as investigations of the impact of hydrodynamic frame on the causality and stability properties of Bjorken flow, planar shockwave, and heat flow solutions.

Additional Information

© 2022 American Physical Society. This material is based upon work supported by the National Science Foundation (NSF) Graduate Research Fellowship Program under Grant No. DGE-1656466. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. F. P. acknowledges support from NSF Grant No. PHY-2207286, the Simons Foundation, and the Canadian Institute For Advanced Research (CIFAR). E. R. M. acknowledges support from postdoctoral fellowships at the Princeton Center for Theoretical Science, the Princeton Gravity Initiative, and the Institute for Advanced Study.

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Created:
August 20, 2023
Modified:
October 23, 2023