Spatial averaging and apparent acceleration in inhomogeneous spaces
  As an alternative to dark energy that explains the observed acceleration of
the universe, it has been suggested that we may be at the center of an
inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB)
solution of Einstein's field equations. To test this possibility, it is
necessary to solve the null geodesics. In this paper we first give a detailed
derivation of a fully analytical set of differential equations for the radial
null geodesics as functions of the redshift in LTB models. As an application we
use these equaions to show that a positive averaged acceleration $a_D$ obtained
in LTB models through spatial averaging can be incompatible with cosmological
observations. We provide examples of LTB models with positive $a_D$ which fail
to reproduce the observed luminosity distance $D_L(z)$. Since the apparent
cosmic acceleration $a^{FLRW}$ is obtained from fitting the observed luminosity
distance to a FLRW model we conclude that in general a positive $a_D$ in LTB
models does not imply a positive $a^{FLRW}$.
