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Title: An exact Jacobi map in the geodesic light-cone gauge

Abstract

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]
  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)
Publication Date:
OSTI Identifier:
22369945
Resource Type:
Journal Article
Journal Name:
Journal of Cosmology and Astroparticle Physics
Additional Journal Information:
Journal Volume: 2013; Journal Issue: 11; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1475-7516
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COORDINATES; DISTANCE; EQUATIONS; LIGHT CONE; LUMINOSITY; MAPS; RED SHIFT; SIGNALS

Citation Formats

Fanizza, G., Gasperini, M., Marozzi, G., and Veneziano, G., E-mail: Giuseppe.Fanizza@ba.infn.it, E-mail: Maurizio.Gasperini@ba.infn.it, E-mail: Giovanni.Marozzi@unige.ch, E-mail: Gabriele.Veneziano@cern.ch. An exact Jacobi map in the geodesic light-cone gauge. United States: N. p., 2013. Web. doi:10.1088/1475-7516/2013/11/019.
Fanizza, G., Gasperini, M., Marozzi, G., & Veneziano, G., E-mail: Giuseppe.Fanizza@ba.infn.it, E-mail: Maurizio.Gasperini@ba.infn.it, E-mail: Giovanni.Marozzi@unige.ch, E-mail: Gabriele.Veneziano@cern.ch. An exact Jacobi map in the geodesic light-cone gauge. United States. https://doi.org/10.1088/1475-7516/2013/11/019
Fanizza, G., Gasperini, M., Marozzi, G., and Veneziano, G., E-mail: Giuseppe.Fanizza@ba.infn.it, E-mail: Maurizio.Gasperini@ba.infn.it, E-mail: Giovanni.Marozzi@unige.ch, E-mail: Gabriele.Veneziano@cern.ch. 2013. "An exact Jacobi map in the geodesic light-cone gauge". United States. https://doi.org/10.1088/1475-7516/2013/11/019.
@article{osti_22369945,
title = {An exact Jacobi map in the geodesic light-cone gauge},
author = {Fanizza, G. and Gasperini, M. and Marozzi, G. and Veneziano, G., E-mail: Giuseppe.Fanizza@ba.infn.it, E-mail: Maurizio.Gasperini@ba.infn.it, E-mail: Giovanni.Marozzi@unige.ch, E-mail: Gabriele.Veneziano@cern.ch},
abstractNote = {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.},
doi = {10.1088/1475-7516/2013/11/019},
url = {https://www.osti.gov/biblio/22369945}, journal = {Journal of Cosmology and Astroparticle Physics},
issn = {1475-7516},
number = 11,
volume = 2013,
place = {United States},
year = {Fri Nov 01 00:00:00 EDT 2013},
month = {Fri Nov 01 00:00:00 EDT 2013}
}