Light-Cone Observables and Gauge-Invariance in the Geodesic Light-Cone
  Formalism
  The remarkable properties of the geodesic light-cone (GLC) coordinates allow
analytic expressions for the light-cone observables, providing a new
non-perturbative way for calculating the effects of inhomogeneities in our
Universe. However, the gauge-invariance of these expressions in the GLC
formalism has not been shown explicitly. Here we provide this missing part of
the GLC formalism by proving the gauge-invariance of the GLC expressions for
the light-cone observables, such as the observed redshift, the luminosity
distance, and the physical area and volume of the observed sources. Our study
provides a new insight on the properties of the GLC coordinates and it
complements the previous work by the GLC collaboration, leading to a
comprehensive description of light propagation in the GLC representation.
