Testing homogeneity with galaxy number counts : light-cone metric and
  general low-redshift expansion for a central observer in a matter dominated
  isotropic universe without cosmological constant
  As an alternative to dark energy 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. In order to
test this hypothesis we calculate the general analytical formula to fifth order
for the redshift spherical shell mass. Using the same analytical method we
write the metric in the light-cone by introducing a gauge invariant quantity
$G(z)$ which together with the luminosity distance $D_L(z)$ completely
determine the light-cone geometry of a LTB model.
