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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 \Lambda.
F. Kottler “Über die physikalischen Grundlagen der Einsteinschen Gravitationstheorie”, Ann. Phys. (Berlin), 56
1918
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L. P. Eisenhart, Riemannian Geometry
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J. L. Synge, Relativity: The General Theory
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G.C. McVittie, Mon. Not. R. Astron. Soc. 93, 325 (1933); see also G. C. McVittie, General Relativity and Cosmology
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P. J. Topalov and V. S. Matveev, “Geodesic equivalence and integrability”, arXiv:math.DG/9911062
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V. S. Matveev and P. J. Topalov, “Quantum integrability of Beltrami-Laplace operator as geodesic equivalence”, Math. Z. 238
2001
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2008
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M. Park, “Rigorous approach to gravitational lensing,” Phys. Rev. D 78
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