Critique of the use of geodesics in astrophysics and cosmology
  Since particles obey wave equations, in general one is not free to postulate
that particles move on the geodesics associated with test particles. Rather,
for this to be the case one has to be able to derive such behavior starting
from the equations of motion that the particles obey, and to do so one can
employ the eikonal approximation. To see what kind of trajectories might occur
we explore the domain of support of the propagators associated with the wave
equations. For a minimally coupled massless scalar field the domain of support
in curved space is shown to not be restricted to the light cone, while for a
conformally coupled massless scalar field the curved space domain is only
restricted to the light cone if it propagates in a conformal to flat
background. Consequently, eikonalization does not in general lead to null
geodesics for curved space massless rays even though it does lead to straight
line trajectories in flat spacetime. Equal remarks apply to the massless
conformal invariant Maxwell equations. However, for massive particles one does
obtain standard geodesic behavior this way, since they do not propagate on the
light cone to begin with. Thus depending on how big the curvature actually is,
in principle, even if not necessarily in practice, the standard
null-geodesic-based gravitational bending formula and the general behavior of
propagating light rays are in need of modification in regions with high enough
curvature. We show that relativistic eikonalization has an intrinsic
light-front structure, and show that eikonalization in a theory with local
conformal symmetry leads to trajectories that are only globally conformally
symmetric. Normals to wavefronts follow the eikonal trajectories, with these
trajectories being the trajectories along which energy and momentum are
transported.
