Abstract
It is shown how a simple property of straight lines in flat space allows us to define ‘triangulation lines’ in any space with axial symmetry. This definition is invariant under coordinate transformation provided we use the symmetry group to define the angular coordinate ϕ. Triangulation lines possess many of the properties of straight lines in Euclidean geometry; in particular, the sum of the angles of a triangle whose sides are triangulation lines is equal to π. Their geometrical properties make these lines especially suitable as reference lines with respect to which the bending of any curve — e.g., a photon track in a stationary, axisymmetric space-time, can be measured.
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References
Brandt, V. E.: 1975,Soviet Astron. AJ 18, 649.
McCrea, W. H.: 1979,Quart. J. Roy. Astron. Soc. 20, 251.
Mikhailov, A. A.: 1976,Soviet Astron. AJ 20, 248.
Murray, C. A.: 1981,Monthly Notices Roy. Astron. Soc. 195, 639.
Shapiro, I. I.: 1967,Science 157, 806.
Ward, W.: 1970,Astrophys. J. 162, 345.
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Cowling, S.A. Triangulation lines in stationary space-times with axial symmetry. Astrophys Space Sci 95, 79–85 (1983). https://doi.org/10.1007/BF00661157
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DOI: https://doi.org/10.1007/BF00661157