Light-bending in Schwarzschild-de-Sitter: projective geometry of the optical metric
arXiv:0808.3074 · doi:10.1088/0264-9381/25/24/245009
Abstract
We interpret the well known fact that the equations for light rays in the Kottler or Schwarzschild-de Sitter metric are independent of the cosmological constant in terms of the projective equivalence of the optical metric for any value of Λ. We explain why this does not imply that lensing phenomena are independent of Λ. Motivated by this example, we find a large collection of one-parameter families of projectively equivalent metrics including both the Kottler optical geometry and the constant curvature metrics as special cases. Using standard constructions for geodesically equivalent metrics we find classical and quantum conserved quantities and relate these to known quantities.
8 pages
References in corpus (2)
Cited by in corpus (14)
- Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry
- Aspherical Photon and Anti-Photon Surfaces
- Light paths of normal and phantom Einstein-Maxwell-dilaton black holes
- Beyond lensing by the cosmological constant
- Geodesic equation in non-commutative gauge theory of gravity
- Photon orbits and phase transition for Non-Linear charged Anti-de Sitter black holes
- Ultrastatic spacetimes
- Light from Schwarzschild Black Holes in de Sitter expanding universe
- Light bending by the cosmological constant
- Cosmological applications of the Brown-York quasilocal mass
- Time delay in the Einstein-Straus solution
- Geodesic motion of a test particle around a noncommutative Schwarzchild Anti-de Sitter black hole
- Optical Metrics and Projective Equivalence
- Electromagnetic radiation from circular orbits in Schwarzschild--de Sitter spacetime