A general relativistic kinetic theory approach to linear transport in generic hydrodynamic frame

In this study, we investigate the linear transport of neutral system within the framework of relativistic kinetic theory. Under the relaxation time approximation, we obtain an iterative solution to the relativistic Boltzmann equation in generic stationary spacetime. This solution provides a scheme to study non-equilibrium system order by order. Our calculations are performed in generic hydrodynamic frame, and the results can be reduced to a specific hydrodynamic frame by imposing constraints. As a specific example, we analytically calculated the covariant expressions of the particle flow and the energy momentum tensor up to the first order in relaxation time. Finally and most importantly, we present all 14 kinetic coefficients for a neutral system, which are verified to satisfy the Onsager reciprocal relation in a generic hydrodynamic frame and guarantee a non-negative entropy production in the frame where the first order conservation laws are restored.