Geometrical optics in general relativity

Preprint English OPEN
Loinger, A.;
(2006)
  • Subject: Physics - General Physics
    arxiv: General Relativity and Quantum Cosmology | Physics::General Physics

General relativity includes geometrical optics. This basic fact has relevant consequences that concern the physical meaning of the discontinuity surfaces propagated in the gravitational field - as it was first emphasized by Levi-Civita.
  • 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 (Springer-Verlag, Berlin) 1935, p.258.

    [6] a) D. Hilbert [5]; b) T. Levi-Civita, 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 Levi-Civita on light reflection and refraction, see T. Levi-Civita, Atti Pont. Acc. Sci. Nuovi Lincei, a.LXXXIV (1930-31) 332 - also in Opere matematiche - Memorie e Note, Vol.5 ◦ (Zanichelli, Bologna) 1970, p.157. Indeed, Levi-Civita adopts a phenomenological point of view, based on an unanalyzed notion of refractive index, in full analogy with a known pre-relativistic treatment, see e.g. T. Levi-Civita 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) E-mail address: angelo.loinger@mi.infn.it

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