Jeans instability analysis in the presence of heat in Eckart’s frame

Abstract

It is shown that the coupling of heat with acceleration first proposed by Eckart would have an overwhelming effect in the growth of density mass fluctuations, even in non-relativistic fluids in the presence of a gravitational field. Gravitational effects would be negligible if the heat-acceleration relation is assumed to be valid for the hydrodynamic equations. A direct implication of this result is that recent alternative first order in the gradients theories must be taken into account while describing a special relativistic fluid.

Structure formation in the presence of relativistic heat conduction: corrections to the Jeans wave number with a stable, first order in the gradients, formalism

“…At this stage it is convenient to point out that in previous work the dispersion relation obtained was a fourth order polynomial with a dominating positive root which eliminates any possibility of structure formation in the system [8]. On the other hand, the use of Eq.…”

“…Since, to first order in fluctuations, the continuity and heat equations, Eqs. (8) and (10), are only coupled through the divergence of the velocity fluctuations δθ, it is convenient to calculate the divergence and curl of the momentum balance equation, Eq. (9).…”

“…In Ref. [8] it was clearly shown that if Eckart's closure is introduced in the transport equations, the gravitational instability is not present in the system, even in the non-relativistic limit. On the other hand, what has been shown here is that by introducing the constitutive equation obtained in Refs.…”

“…In recent work, two of us addressed the question of structure formation in relativistic dilute gases in the presence of dissipation introducing Eckart's equation for the heat flux [8]. In a high temperature dilute gas, the typical molecular speeds are close to the speed of light, thus special relativistic effects need to be taken into account.…”

Sobre el flujo de calor en el tensor energía momento de un fluido relativista

“…El flujo de calor y sus ecuaciones constitutivas en sistemas relativistas han sido el objeto de interpretaciones y discusiones diversas. En el formalismo de Eckart [15] la ecuación constitutiva del flujo de calor contiene un término de aceleración que parece ser la fuente de importantes inestabilidades en las fluctuaciones alrededor del equilibrio [16,17], lo que implica, entre otras cosas, que el agua a temperatura ambiente se vuelve inestable [18], además de la no existencia del espectro de Rayleigh-Brillouin [19] y la desaparición de la inestabilidad de Jeans responsable de la formación de estructura [20,21].…”