Optical Metrics and Projective Equivalence

Details Optical Metrics and Projective Equivalence Optical Metrics and Projective Equivalence

2011-01-23

arxiv.org/abs/1101.4375v2

Phys.Rev.D83:084047,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, two figures, final version, to appear in Physical Review D

Scientific paper

10.1103/PhysRevD.83.084047

Trajectories of light rays in a static spacetime are described by unparametrised 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 time--like 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.

Affiliated with

Also associated with

No associations

Rating

Optical Metrics and Projective Equivalence does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Optical Metrics and Projective Equivalence, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Optical Metrics and Projective Equivalence will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-587255