Geometrical optics in general relativity

Subject: Physics  General Physicsarxiv: General Relativity and Quantum Cosmology  Physics::General Physics

References
(9)
[1] A. Loinger, “Relativity and wavy motions”, in course of publication on Spacetime & Substance; also in arXiv:physics/0603214 v1 (March 25th, 2006).
[2] A. Sommerfeld and I. Runge, Ann. Physik, 35 (1911) 277; see also Sommerfeld's Optik, Zweite Auflage (Akad. Verlagsges., Leipzig) 1959; p.187 ff.  Cf. further: R.K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, etc.) 1964; M. Kline and J.W. Kay, Electromagnetic Theory and Geometrical Optics (Interscience Publishers, New York) 1965.
[3] Cf. e.g.: H. Bateman, Partial Differential Equations of Mathematical Physics (Dover Publications, New York) 1932; H.F. Weinberger, A First Course in Partial Differential Equations  with Complex Variables and Transformation Methods (Blaisdell Publ. Company, Waltham, Mass.; etc.) 1965.  See also Luneburg [2], and Kline and Kay [2].
[4] V. Fock, The Theory of Space, Time and Gravitation, 2nd revised edition (Pergamon Press, Oxford, etc.) 1964, Chapts.I and III, and App.F.
[5] D. Hilbert, Mathem. Annalen, 92 (1924) 1; reprinted in Gesammelte Abhandlungen, Dritter Band (SpringerVerlag, Berlin) 1935, p.258.
[6] a) D. Hilbert [5]; b) T. LeviCivita, Rend. Acc. Lincei, 11 (s.6a) (1930) 3 and 113, reprinted in Opere matematiche  Memorie e Note, Vol. 5 ◦ (Zanichelli, Bologna) 1970, p.77 and p.87; c) V. Fock [4], p.133 and ff.
[7] E.T. Whittaker, Proc. Cambridge Phil. Soc., 24/1 (1927) 32.
[8] A. Loinger, arXiv:physics/0606019 v1 (June 2nd, 2006), in course of publication on Spacetime & Substance.
[9] W. Gordon, Ann. Physik, 72 (1923) 421. In Part IV of this article the Author discusses the geometrical optics as a consequence of the previous e.m. equations for ponderable media. Remark that his results are not at variance with the results by LeviCivita on light reflection and refraction, see T. LeviCivita, Atti Pont. Acc. Sci. Nuovi Lincei, a.LXXXIV (193031) 332  also in Opere matematiche  Memorie e Note, Vol.5 ◦ (Zanichelli, Bologna) 1970, p.157. Indeed, LeviCivita adopts a phenomenological point of view, based on an unanalyzed notion of refractive index, in full analogy with a known prerelativistic treatment, see e.g. T. LeviCivita e U. Amaldi, Lezioni di meccanica razionale, Vol.II/2 (Zanichelli, Bologna) 1927, p.515 ff. Dipartimento di Fisica, Universita` di Milano, Via Celoria, 16  20133 Milano (Italy) Email address: angelo.loinger@mi.infn.it

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