Stability, causality, and hyperbolicity in Carter's regular'' theory of relativistic heat-conducting fluids

Journal Article · Fri Jun 15 00:00:00 EDT 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.41.3687· OSTI ID:6734595

Olson, T S; Hiscock, W A ^[1]

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1. Department of Physics, Montana State University, Bozeman, Montana 59717 (USA)

Stability and causality are studied for linear perturbations about equilibrium in Carter's regular'' theory of relativistic heat-conducting fluids. The regular'' theory, when linearized around an equilibrium state having vanishing expansion and shear, is shown to be equivalent to the inviscid limit of the linearized Israel-Stewart theory of relativistic dissipative fluids for a particular choice of the second-order coefficients {beta}{sub 1} and {gamma}{sub 2}. A set of stability conditions is determined for linear perturbations of a general inviscid Israel-Stewart fluid using a monotonically decreasing energy functional. It is shown that, as in the viscous case, stability implies that the characteristic velocities are subluminal and that perturbations obey hyperbolic equations. The converse theorem is also true. We then apply this analysis to a nonrelativistic Boltzmann gas and to a strongly degenerate free Fermi gas in the regular'' theory. Carter's regular'' theory is shown to be incapable of correctly describing the nonrelativistic Boltzmann gas and the degenerate Fermi gas (at all temperatures).

• OSTI ID: 6734595
• Journal Information: Physical Review, D (Particles Fields); (USA), Vol. 41:12; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
FERMI GAS
CAUSALITY
THERMAL CONDUCTION
COUPLING CONSTANTS
DISSIPATION FACTOR
EQUATIONS OF MOTION
PERTURBATION THEORY
RELATIVITY THEORY
STABILITY
THERMODYNAMIC PROPERTIES
DIFFERENTIAL EQUATIONS
ENERGY TRANSFER
EQUATIONS
FIELD THEORIES
FLUIDS
GASES
GENERAL RELATIVITY THEORY
HEAT TRANSFER
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics