  A mixture of relativistic gases of non-disparate rest masses in a
Schwarzschild metric is studied on the basis of a relativistic Boltzmann
equation in the presence of gravitational fields. A BGK-type model equation of
the collision operator of the Boltzmann equation is used in order to compute
the non-equilibrium distribution functions by the Chapman-Enskog method. The
main focus of this work is to obtain Fick's law without the thermal-diffusion
cross-effect. Fick's law has four contributions, two of them are the usual
terms proportional to the gradients of concentration and pressure. The other
two are of the same nature as those which appears in Fourier's law in the
presence of gravitational fields and are related with an acceleration and
gravitational potential gradient, but unlike Fourier's law these two last terms
are of non-relativistic order. Furthermore, it is shown that the coefficients
of diffusion depend on the gravitational potential and they become larger than
those in the absence of it.
