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