Light rays in gravitating and refractive media: A comparison of the field to particle and Hamiltonian approaches

The field-to-particle method of H. P. Robertson as applied by Noonan, in order to obtain the general relativistic equations describing the trajectory of a photon in a refractive medium, is compared with Synge’s general relativistic Hamiltonian theory of waves and rays. For a photon in vacuum it is known that both approaches yield the same equation for the trajectory, i.e., a null geodesic. However for a photon in a medium, in contradistinction to the Hamiltonian theory, the field-to-particle method (a) yields equations of the photon trajectory valid only in a nondispersive medium, (b) the time component u⁰ of the tangent to the ray remains an undetermined quantity, (c) agreement with the Hamiltonian theory is achieved by substituting into Noonan’s equations the Hamiltonian expression for u ⁰. Published in Astrofizika, Vol. 42, No. 3, pp. 449–455, July–September, 1999.