  A relativistic gas in a Schwarzschild metric is studied within the framework
of a relativistic Boltzmann equation in the presence of gravitational fields,
where Marle's model for the collision operator of the Boltzmann equation is
employed. The transport coefficients of bulk and shear viscosities and thermal
conductivity are determined from the Chapman-Enskog method. It is shown that
the transport coefficients depend on the gravitational potential. Expressions
for the transport coefficients in the presence of weak gravitational fields in
the non-relativistic (low temperatures) and ultra-relativistic (high
temperatures) limiting cases are given. Apart from the temperature gradient the
heat flux has two relativistic terms. The first one, proposed by Eckart, is due
to the inertia of energy and represents an isothermal heat flux when matter is
accelerated. The other, suggested by Tolman, is proportional to the
gravitational potential gradient and indicates that -- in the absence of an
acceleration field -- a state of equilibrium of a relativistic gas in a
gravitational field can be attained only if the temperature gradient is
counterbalanced by a gravitational potential gradient.
