TY - JOUR
T1 - Nonlinear causality of general first-order relativistic viscous hydrodynamics
AU - Bemfica, Fábio S.
AU - Disconzi, Marcelo M.
AU - Noronha, Jorge
N1 - We thank P. Kovtun for showing the results of Ref. to us before submission. F.\u2009S.\u2009B. is partially supported by a Discovery Grant administered by Vanderbilt University. Part of this work was done while F.\u2009S.\u2009B. was visiting Vanderbilt University. M.\u2009M.\u2009D. is partially supported by a Sloan Research Fellowship provided by the Alfred P. Sloan foundation, NSF Grant No. DMS-1812826, a Discovery Grant administered by Vanderbilt University, and a Dean\u2019s Faculty Fellowship. J.\u2009N. was partially supported by CNPq Grant No. 306795/2017-5 and FAPESP Grant No. 2017/05685-2.
PY - 2019/11/11
Y1 - 2019/11/11
N2 - Effective theory arguments are used to derive the most general energy-momentum tensor of a relativistic viscous fluid with an arbitrary equation of state (in the absence of other conserved currents) that is first-order in the derivatives of the energy density and flow velocity and does not include extended variables such as in Mueller-Israel-Stewart-like theories. This energy-momentum tensor leads to a causal theory, provided one abandons the usual conventions for the out-of-equilibrium hydrodynamic variables put forward by Landau-Lifshitz and Eckart. In particular, causality requires nonzero out-of-equilibrium energy density corrections and heat flow. Conditions are found to ensure linear stability around equilibrium in flat space-time. We also prove local existence and uniqueness of solutions to the equations of motion. Our causality, existence, and uniqueness results hold in the full nonlinear regime, without symmetry assumptions, in four space-time dimensions, with or without coupling to Einstein's equations, and are mathematically rigorously established. Furthermore, a kinetic theory realization of this energy-momentum tensor is also provided.
AB - Effective theory arguments are used to derive the most general energy-momentum tensor of a relativistic viscous fluid with an arbitrary equation of state (in the absence of other conserved currents) that is first-order in the derivatives of the energy density and flow velocity and does not include extended variables such as in Mueller-Israel-Stewart-like theories. This energy-momentum tensor leads to a causal theory, provided one abandons the usual conventions for the out-of-equilibrium hydrodynamic variables put forward by Landau-Lifshitz and Eckart. In particular, causality requires nonzero out-of-equilibrium energy density corrections and heat flow. Conditions are found to ensure linear stability around equilibrium in flat space-time. We also prove local existence and uniqueness of solutions to the equations of motion. Our causality, existence, and uniqueness results hold in the full nonlinear regime, without symmetry assumptions, in four space-time dimensions, with or without coupling to Einstein's equations, and are mathematically rigorously established. Furthermore, a kinetic theory realization of this energy-momentum tensor is also provided.
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U2 - 10.1103/PhysRevD.100.104020
DO - 10.1103/PhysRevD.100.104020
M3 - Article
AN - SCOPUS:85075296365
SN - 2470-0010
VL - 100
JO - Physical Review D
JF - Physical Review D
IS - 10
M1 - 104020
ER -