  We present a combined analytical and numerical study of the early stages
(sub-100fs) of the non-equilibrium dynamics of photo-excited electrons in
graphene. We employ the semiclassical Boltzmann equation with a collision
integral that includes contributions from electron-electron (e-e) and
electron-optical phonon interactions. Taking advantage of circular symmetry and
employing the massless Dirac Fermion (MDF) Hamiltonian, we are able to perform
an essentially analytical study of the e-e contribution to the collision
integral. This allows us to take particular care of subtle collinear scattering
processes - processes in which incoming and outgoing momenta of the scattering
particles lie on the same line - including carrier multiplication (CM) and
Auger recombination (AR). These processes have a vanishing phase space for two
dimensional MDF bare bands. However, we argue that electron-lifetime effects,
seen in experiments based on angle-resolved photoemission spectroscopy, provide
a natural pathway to regularize this pathology, yielding a finite contribution
due to CM and AR to the Coulomb collision integral. Finally, we discuss in
detail the role of physics beyond the Fermi golden rule by including screening
in the matrix element of the Coulomb interaction at the level of the Random
Phase Approximation (RPA), focusing in particular on the consequences of
various approximations including static RPA screening, which maximizes the
impact of CM and AR processes, and dynamical RPA screening, which completely
suppresses them.
