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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 JarvisThis 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 SocietyVolume
409Pagination
953-962ISSN
0035-8711Department/School
School of Natural SciencesPublisher
Blackwell Publishing LtdPlace of publication
9600 Garsington Rd, Oxford, England, Oxon, Ox4 2DgRights statement
The definitive published version is available online at: http://onlinelibrary.wiley.com/Repository Status
- Restricted