The generic instability of relativistic fluids revisited: transverse mode fluctuations and diffussion fluxes in the Landau-Lifshitz frame

Stability of statistical fluctuations of relativistic fluids is a classical problem that has been addressed since the pioneering works of Hisckock and Lindblom back en 1985, who identified exponential growths of statistical fluctuations using a phenomenological approach. In the present work we critically examine the role played by the heat flux in the onset of this type of instability using the Landau-Lifschitz frame, in which the dissipative contributions to this variable are not contained in the spatial components of the energy-momentum tensor. It is shown that the generic instabilities in the transverse mode are eliminated if the corresponding constitutive equations are established within a first order in the gradients approximation kinetic theory formalism, and that purely relativistic dissipative contributions to the diffusive fluxes arise the aforementioned frame.