Thermal conduction in systems out of hydrostatic equilibrium

Abstract

We analyse the effects of thermal conduction in a relativistic fluid, just after its departure from hydrostatic equilibrium, on a time scale of the order of thermal relaxation time. It is obtained that the resulting evolution will critically depend on a parameter defined in terms of thermodynamic variables, which is constrained by causality requirements

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“…In fact, as it is shown in [1,2], if the system reaches the critical point (α = 1), then the inertial mass term vanishes. Furthermore it can be shown that conditions ensuring stability and causality [13,14] are violated at the critical point [2].…”

“…In [1] it appears that a parameter α formed by a specific combination of thermal conductivity coefficient κ, relaxation time τ , temperature T , proper energy density ρ and pressure p, α = κT τ (ρ + p) , may critically affect the evolution of the object. Specifically, it was shown that in the equation of motion of any fluid element, the inertial mass density term vanishes for α = 1 (critical point) and is negative beyond that value.…”

“…In others (pure thermal conduction) [1,2], later requirements are violated slightly below the critical point.…”

Hyperbolic theories of dissipation: Why and when do we need them?

“…Indeed, it has been shown [31] that after the fluid leaves the equilibrium, on a time scale of the order of relaxation time, the effective inertial mass density of a dissipative fluid reduces by a factor that depends on the dissipative variables. By "effective inertial mass density" (EIMD) we mean the factor of proportionality between the applied three-force density and the corresponding proper acceleration (i.e., the three-acceleration measured in the instantaneous rest frame).…”

A Study of Charged Cylindrical Gravitational Collapse with Dissipative Fluid

“…Further, combination of all these terms on the r.h.s of (49) results in the l.h.s, that is, (1 − )( + − 4 / √ 3) < 0; there will be gravitational collapse, while there will be expansion if the l.h.s is to be positive. It should be mentioned that such effects were first discussed by Herrera et al [37] in context of thermal conduction in hydrostatic equilibrium. Interestingly, if continuously decreases from a value larger than unity to one less than unity, then there will be a phase transition (collapse to expansion) and bounce will occur.…”