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Title: 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 geodesic-deviation equation, and thus to derive an exact expression for the Jacobi map J{sup A}{sub B}(s,o) connecting a generic source s to a geodesic observer o in a generic space time. In this gauge J{sup A}{sub 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{sup A}{sub 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.
Authors:
;  [1] ;  [2] ;  [3]
  1. Dipartimento di Fisica, Università di Bari, Via G. Amendola 173, 70126 Bari (Italy)
  2. Université de Gèneve, Département de Physique Théorique and CAP, 24 quai Ernest-Ansermet, CH-1211 Genève 4 (Switzerland)
  3. Collège de France, 11 place Marcelin Berthelot, 75005 Paris (France)
Publication Date:
OSTI Identifier:
22369945
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2013; Journal Issue: 11; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COORDINATES; DISTANCE; EQUATIONS; LIGHT CONE; LUMINOSITY; MAPS; RED SHIFT; SIGNALS