  A covariant scattering kernel is a core component in any self-consistent
general relativistic radiative transfer formulation in scattering media. An
explicit closed-form expression for a covariant Compton scattering kernel with
a good dynamical energy range has unfortunately not been available thus far.
Such an expression is essential to obtain numerical solutions to the general
relativistic radiative transfer equations in complicated astrophysical settings
where strong scattering effects are coupled with highly relativistic flows and
steep gravitational gradients. Moreover, this must be performed in an efficient
manner. With a self-consistent covariant approach, we have derived a
closed-form expression for the Compton scattering kernel for arbitrary energy
range. The scattering kernel and its angular moments are expressed in terms of
hypergeometric functions, and their derivations are shown explicitly in this
paper. We also evaluate the kernel and its moments numerically, assessing
various techniques for their calculation. Finally, we demonstrate that our
closed-form expression produces the same results as previous calculations,
which employ fully numerical computation methods and are applicable only in
more restrictive settings.
