Effects of anisotropy on gravitational infall in galaxy clusters using
  an exact general relativistic model
  We study the effects and implications of anisotropies at the scale of galaxy
clusters by building an exact general relativistic model of a cluster using the
inhomogeneous and anisotropic Szekeres metric. The model is built from a
modified Navarro-Frenk-White (NFW) density profile. We compare this to a
corresponding spherically symmetric structure in the Lemaitre-Tolman (LT) model
and quantify the impact of introducing varying levels of anisotropy. We examine
two physical measures of gravitational infall -- the growth rate of density and
the velocity of the source dust in the model. We introduce a generalization of
the LT dust velocity profile for the Szekeres metric and demonstrate its
consistency with the growth rate of density. We find that the growth rate of
density in one substructure increases by 0.5%, 1.5%, and 3.75% for 5%, 10%, and
15% levels of introduced anisotropy, which is measured as the fractional
displaced mass relative to the spherically symmetric case. The infall velocity
of the dust is found to increase by 2.5, 10, and 20 km/s (0.5%, 2%, and 4.5%),
respectively, for the same three levels of anisotropy. This response to the
anisotropy in a structure is found to be strongly nonlinear with respect to the
strength of anisotropy. These relative velocities correspond to an equivalent
increase in the total mass of the spherically symmetric structure of 1%, 3.8%,
and 8.4%, indicating that not accounting for the presence of anisotropic mass
distributions in cluster models can strongly bias the determination of physical
properties like the total mass.
