General relativistic Boltzmann equation, II: Manifestly covariant treatment

In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p2=m2c2. Due to this restriction, the resulting Boltzmann equation, although covariant, turned out to be not manifestly covariant. In the present article we switch from mass-shell momenta to off-shell momenta, and thereby arrive at a Boltzmann equation that is manifestly covariant.