The optical-mechanical analogy in general relativity: Exact Newtonian forms for the equations of motion of particles and photons

Details The optical-mechanical analogy in general relativity: Exact Newtonian forms for the equations of motion of particles and photons The optical-mechanical analogy in general relativity: Exact Newtonian forms for the equations of motion of particles and photons

Apr 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996gregr..28..413e&link_type=abstract

General Relativity and Gravitation, Volume 28, Issue 4, pp.413-439

Physics

23

Scientific paper

In many metrics of physical interest, the gravitational field can be represented as an optical medium with an effective index of refraction. We show that, in such a metric, the orbits of both massive and massless particles are governed by a variational principle which involves the index of refraction and which assumes the form of Fermat's principle or of Maupertuis's principle. From this variational principle we derive exact equations of motion of Newtonian form which govern both massless and massive particles. These equations of motion are applied to some problems of physical interest.

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