Abstract
Attention is drawn to the advantages of representing dynamical behavior in a stationary or static background spacetime in terms of a fixed reference 3-geometry that differs from the usual one by a certain conformal rescaling factor. The resulting Riemannian metric may be appropriately described as the “optical geometry” in recognition of the fact that “line-of-sight” trajectories are faithfully represented within it as geodesic, at least in the strictly static case for which such “lines-of-sight” are unambiguously defined. (In more general stationary examples the geodesies represent what amounts to the result of a cancellation between the Coriolis-type effects that would cause a physical light path to deviate to one side or the other depending on the sense of propagation.) The application to the particular case of the Schwarzschild solution is discussed: In this example the optical 3-geometry has a throat that occurs not on the horizon (as in the directly projected 3-geometry) but at the radius of the circular null geodesic orbit.
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References
Scherk, J., and Schwarz, J. (1979).Nucl. Phys. B,153, 61.
Breitenlohner, P., Maison, D., and Gibbons, G. (1986).4-Dimensional Black Holes from Kaluza-Klein Theory, preprint (DAMPT, Cambridge).
Carter, B. (1988).J. Math. Phys.,29, 224.
Bardeen, J. M. (1973).Timelike and Null Geodesies in Kerr Metric in Black Holes, 1972 Les Houches Summer School, B. DeWitt and C. DeWitt, eds. (Gordon and Breach, New York).
Shapiro, S. L., and Teukolsky, S. A. (1983).Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects (John Wiley & Sons, New York).
Demiański, M. (1985).Relativistic Astrophysics (Pergamon, Oxford).
Abramowicz, M. A., and Lasota, J. P. (1974).Acta Phys. Pol. B,5, 327.
Abramowicz, M. A., and Lasota, J. P. (1986).Am. J. Phys.,54, 936.
De Felice, F. (1971).Gen. Rel. Grav.,2, 347.
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Abramowicz, M.A., Carter, B. & Lasota, J.P. Optical reference geometry for stationary and static dynamics. Gen Relat Gravit 20, 1173–1183 (1988). https://doi.org/10.1007/BF00758937
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DOI: https://doi.org/10.1007/BF00758937