An exact Jacobi map in the geodesic light-cone gauge
  The remarkable properties of the recently proposed geodesic light-cone (GLC)
gauge allow to explicitly solve the geodetic-deviation equation, and thus to
derive an exact expression for the Jacobi map J^A_B(s,o) connecting a generic
source s to a geodesic observer o in a generic space time. In this gauge J^A_B
factorizes into the product of a local quantity at s times one at o, implying
similarly factorized expressions for the area and luminosity distance. In any
other coordinate system J^A_B is simply given by expressing the GLC quantities
in terms of the corresponding ones in the new coordinates. This is explicitly
done, at first and second order, respectively, for the synchronous and Poisson
gauge-fixing of a perturbed, spatially-flat cosmological background, and the
consistency of the two outcomes is checked. Our results slightly amend previous
calculations of the luminosity-redshift relation and suggest a possible
non-perturbative way for computing the effects of inhomogeneities on
observations based on light-like signals.
