Journal Article

A kinematical approach to gravitational lensing using new formulae for refractive index and acceleration

S. J. Walters, L. K. Forbes and P. D. Jarvis

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 409, issue 3, pages 953-962
Published in print December 2010 | ISSN: 0035-8711
Published online December 2010 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2010.17380.x
A kinematical approach to gravitational lensing using new formulae for refractive index and acceleration

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This paper uses the Schwarzschild metric to derive an effective refractive index and acceleration vector that account for relativistic deflection of light rays in an otherwise classical kinematic framework. The new refractive index and the known path equation are integrated to give accurate results for travel time and deflection angle, respectively. A new formula for coordinate acceleration is derived which describes the path of a massless test particle in the vicinity of a spherically symmetric mass density distribution. A standard ray shooting technique is used to compare the deflection angle and time delay predicted by this new formula with the previously calculated values, and with standard first-order approximations. Finally, the ray shooting method is used in theoretical examples of strong and weak lensing, reproducing known observer-plane caustic patterns for multiple masses.

Keywords: acceleration of particles; gravitation; gravitational lensing: strong; gravitational lensing: micro; methods: numerical; planets and satellites: detection

Journal Article.  4759 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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