On the role of shear in cosmological averaging
  Using the spherically symmetric inhomogeneous Lemaitre-Tolman-Bondi dust
solution, we study how the shear and the backreaction depend on the sharpness
of the spatial transition between voids and walls and on the size of the voids.
The voids considered here are regions with matter density Omega ~ 0 and
expansion rate Ht ~ 1, while the walls are regions with matter density Omega ~
1 and expansion rate Ht ~ 2/3. The results indicate that both the
volume-average shear and the variance of the expansion rate grow proportional
to the sharpness of the transition and diverge in the limit of a step function,
but, for realistic-sized voids, are virtually independent of the size of the
void. However, the backreaction, given by the difference of the variance and
the shear, has a finite value in the step-function limit. By comparing the
exact result for the backreaction to the case where the shear is neglected by
treating the voids and walls as separate Friedmann-Robertson-Walker models, we
find that the shear suppresses the backreaction by a factor of (r_0/t_0)^2, the
squared ratio of the void size to the horizon size. This exemplifies the
importance of using the exact solution for the interface between the regions of
different expansion rates and densities. The suppression is justified to hold
also for a network of compensated voids, but may not hold if the universe is
dominated by uncompensated voids.
