  We study charge ordered solutions for fermions on a square lattice
interacting with dynamic antiferromagnetic fluctuations. Our approach is based
on real space Eliashberg equations which are solved self-consistently. We first
show that the antiferromagnetic fluctuations can induce arc features in the
spectral functions, as spectral weight is suppressed at the hot spots; however,
no real pseudogap is generated. At low temperature spontaneous charge order
with a $d$-form factor can be stabilized for certain parameters. As long as the
interacting Fermi surfaces possesses hot spots, the ordering wave vector
corresponds to the diagonal connection of the hot spots, similar to the
non-self-consistent case. Tendencies towards observed axial order only appear
in situations without hot spots.
