The effects of structure anisotropy on lensing observables in an exact
  general relativistic setting for precision cosmology
  The study of relativistic, higher order and nonlinear effects has become
necessary in recent years in the pursuit of precision cosmology. We develop and
apply here a framework to study gravitational lensing in exact models in
general relativity that are not restricted to homogeneity and isotropy, and
where full nonlinearity and relativistic effects are included. We apply the
framework to a specific, anisotropic galaxy cluster model which is based on a
modified NFW halo density profile and described by the Szekeres metric. We
examine the effects of increasing levels of anisotropy in the galaxy cluster on
lensing observables like the convergence and shear for various lensing
geometries, finding a strong nonlinear response in both the convergence and
shear for rays passing through anisotropic regions of the cluster. Deviation
from the expected values in a spherically symmetric structure are asymmetric
with respect to path direction and thus will persist as a statistical effect
when averaged over some ensemble of such clusters. The resulting relative
difference in various geometries can be as large as approximately 2%, 8%, and
24% in the measure of convergence for levels of anisotropy of 5%, 10%, and 15%,
respectively, as a fraction of total cluster mass. For the total magnitude of
shear, the relative difference can grow near the center of the structure to be
as large as 15%, 32%, and 44% for the same levels of anisotropy, averaged over
the two extreme geometries. The convergence is impacted most strongly for rays
which pass in directions along the axis of maximum dipole anisotropy in the
structure, while the shear is most strongly impacted for rays which pass in
directions orthogonal to this axis, as expected. These effects due to
anisotropic structures will affect lensing measurements and must be fully
examined in an era of precision cosmology.
