General Relativity and Gravitation

, Volume 28, Issue 4, pp 413–439 | Cite as

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

  • James Evans
  • Kamal K. Nandi
  • Anwarul Islam


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.


General Relativity Refraction Variational Principle Differential Geometry Gravitational Field 
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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • James Evans
    • 1
  • Kamal K. Nandi
    • 2
  • Anwarul Islam
    • 3
  1. 1.Department of PhysicsUniversity of Puget SoundTacomaUSA
  2. 2.Department of MathematicsUniversity of North BengalDarjeeling (W.B.)India
  3. 3.Department of MathematicsGovernment Tolaram CollegeNarayanganj, DhakaBangladesh

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