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

journal contribution
posted on 2023-05-17, 03:47 authored by Stephen WaltersStephen Walters, Lawrence ForbesLawrence Forbes, Peter JarvisPeter Jarvis
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. Key words: acceleration of particles – gravitation – gravitational lensing: strong – gravitational lensing: micro – methods: numerical – planets and satellites: detection.

History

Publication title

Monthly Notices of the Royal Astronomical Society

Volume

409

Pagination

953-962

ISSN

0035-8711

Department/School

School of Natural Sciences

Publisher

Blackwell Publishing Ltd

Place of publication

9600 Garsington Rd, Oxford, England, Oxon, Ox4 2Dg

Rights statement

The definitive published version is available online at: http://onlinelibrary.wiley.com/

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the physical sciences

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