Optical metrics and projective equivalence
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
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.
- OSTI ID:
- 21541513
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 83, Issue 8; Other Information: DOI: 10.1103/PhysRevD.83.084047; (c) 2011 American Institute of Physics; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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