  We propose a new model for the description of a gravitating multi particle
system, viewed as a kinetic gas. The properties of the, colliding or
non-colliding, particles are encoded into a so called one-particle distribution
function, which is a density on the space of allowed particle positions and
velocities, i.e. on the tangent bundle of the spacetime manifold. We argue that
an appropriate theory of gravity, describing the gravitational field generated
by a kinetic gas, must also be modeled on the tangent bundle. The most natural
mathematical framework for this task is Finsler spacetime geometry. Following
this line of argumentation, we construct a coupling between the kinetic gas and
a recently proposed Finsler geometric extension of general relativity.
Additionally, we explicitly show how the coordinate invariance of the action of
the kinetic gas leads to a novel formulation of conservation of the
energy-momentum distribution of the gas on the tangent bundle.
