Causality and stability conditions of a conformal charged fluid

Abstract

In this paper, I study the conditions imposed on a normal charged fluid so that the causality and stability criteria hold for this fluid. I adopt the newly developed General Frame (GF) notion in the relativistic hydrodynamics framework which states that hydrodynamic frames have to be fixed after applying the stability and causality conditions. To do this, I take a charged conformal matter in the flat and 3 + 1 dimension to analyze better these conditions. The causality condition is applied by looking to the asymptotic velocity of sound hydro modes at the large wave number limit and stability conditions are imposed by looking to the imaginary parts of hydro modes as well as the Routh-Hurwitz criteria. By fixing some of the transports, the suitable spaces for other ones are derived. I observe that in a dense medium having a finite U(1) charge with chemical potential μ0, negative values for transports appear and the second law of thermodynamics has not ruled out the existence of such values. Sign of scalar transports are not limited by any constraints and just a combination of vector transports is limited by the second law of thermodynamic. Also numerically it is proved that the most favorable region for transports $$ {\tilde{\upgamma}}_{1,2}, $$ γ ˜ 1 , 2 , coefficients of the dissipative terms of the current, is of negative values.

Relativistic non-resistive viscous magnetohydrodynamics from the kinetic theory: a relaxation time approach

“…Recently, there are some new developments in the formulation of first-order theories which is potentially causal and stable refs. [48][49][50][51][52][53][54]. However, we note that in the newly developed theory the existence of a relaxation time scale (usually found in the secondorder theories) in the definition of non-equilibrium hydrodynamics variables needs further investigation.…”

First-Order General-Relativistic Viscous Fluid Dynamics

“…In fact, the shear viscosity η and the combination of coefficients that give the bulk viscosity ζ and charge conductivity σ are invariant under first-order field redefinitions, as explained in [62]. Additional constraints among the transport parameters appear when the underlying theory displays conformal invariance, as discussed in [61] at µ = 0, and at finite chemical potential in [62,73] (see also [74]).…”

Constraints on quasinormal modes and bounds for critical points from pole-skipping

“…g . 4 Let us emphasize that this is not a hydrodynamic derivative expansion; equation (3.3) does not pass through the origin. This is a derivative expansion about the n th gapped QNM.…”

“…Stability and causality of distinct formulations of hydrodynamics have been discussed over several decades by now [1] and are still under debate [2][3][4][5][6][7]. One central question is what the convergence radius of the hydrodynamic derivative expansion is when written in momentum space (after a Fourier transformation in a translation-invariant state).…”