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Title: Optical metrics and projective equivalence

Abstract

Trajectories of light rays in a static spacetime are described by unparametrized geodesics of the Riemannian optical metric associated with the Lorentzian spacetime metric. We investigate the uniqueness of this structure and demonstrate that two different observers, moving relative to one another, who both see the Universe as static may determine the geometry of the light rays differently. More specifically, we classify Lorentzian metrics admitting more than one hyper-surface orthogonal timelike Killing vector and analyze the projective equivalence of the resulting optical metrics. These metrics are shown to be projectively equivalent up to diffeomorphism if the static Killing vectors generate a group SL(2,R), but not projectively equivalent in general. We also consider the cosmological C metrics in Einstein-Maxwell theory and demonstrate that optical metrics corresponding to different values of the cosmological constant are projectively equivalent.

Authors:
; ; ;  [1]
  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
Publication Date:
OSTI Identifier:
21541513
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 83; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.83.084047; (c) 2011 American Institute of Physics; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COSMOLOGICAL CONSTANT; EINSTEIN-MAXWELL EQUATIONS; GEODESICS; METRICS; RIEMANN SPACE; SPACE-TIME; SURFACES; TRAJECTORIES; UNIVERSE; EQUATIONS; FIELD EQUATIONS; MATHEMATICAL SPACE; SPACE

Citation Formats

Casey, Stephen, Dunajski, Maciej, Gibbons, Gary, and Warnick, Claude. Optical metrics and projective equivalence. United States: N. p., 2011. Web. doi:10.1103/PHYSREVD.83.084047.
Casey, Stephen, Dunajski, Maciej, Gibbons, Gary, & Warnick, Claude. Optical metrics and projective equivalence. United States. https://doi.org/10.1103/PHYSREVD.83.084047
Casey, Stephen, Dunajski, Maciej, Gibbons, Gary, and Warnick, Claude. 2011. "Optical metrics and projective equivalence". United States. https://doi.org/10.1103/PHYSREVD.83.084047.
@article{osti_21541513,
title = {Optical metrics and projective equivalence},
author = {Casey, Stephen and Dunajski, Maciej and Gibbons, Gary and Warnick, Claude},
abstractNote = {Trajectories of light rays in a static spacetime are described by unparametrized geodesics of the Riemannian optical metric associated with the Lorentzian spacetime metric. We investigate the uniqueness of this structure and demonstrate that two different observers, moving relative to one another, who both see the Universe as static may determine the geometry of the light rays differently. More specifically, we classify Lorentzian metrics admitting more than one hyper-surface orthogonal timelike Killing vector and analyze the projective equivalence of the resulting optical metrics. These metrics are shown to be projectively equivalent up to diffeomorphism if the static Killing vectors generate a group SL(2,R), but not projectively equivalent in general. We also consider the cosmological C metrics in Einstein-Maxwell theory and demonstrate that optical metrics corresponding to different values of the cosmological constant are projectively equivalent.},
doi = {10.1103/PHYSREVD.83.084047},
url = {https://www.osti.gov/biblio/21541513}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 8,
volume = 83,
place = {United States},
year = {Fri Apr 15 00:00:00 EDT 2011},
month = {Fri Apr 15 00:00:00 EDT 2011}
}