G W Gibbons et al 2008 Class. Quantum Grav. 25 245009 doi:10.1088/0264-9381/25/24/245009
G W Gibbons1, C M Warnick1 and M C Werner1,2
Show affiliationsWe 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.
95.30.Sf Relativity and gravitation
02.40.Dr Euclidean and projective geometries
85A40 Cosmology (For relativistic cosmology, see 83F05)
83C40 Gravitational energy and conservation laws; groups of motions
Issue 24 (21 December 2008)
Received 8 September 2008
Published 27 November 2008
G W Gibbons et al 2008 Class. Quantum Grav. 25 245009
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