A Newtonian pre-introduction to gravitational lenses

Abstract

Understanding the deflection of light by a massive deflector, as well as the associated gravitational lens phenomena, require the use of the theory of General Relativity. I consider here a classical analogy, based on Newton's equation of motion for massive particles. These particles are emitted by a distant source and deflected by the gravitational field of a (opaque) star or of a (transparent) galaxy. The dependence of the deviation angle D on the impact parameter b, and the -Euclidean -geometry of the (source, deflector, earth) triplet, imply that different particle trajectories may reach an earth based observer. Since D(b) does not depend on the mass of the particles, a (Newtonian) flavor of gravitational lenses phenomena is naively obtained by setting the particles' velocity equal to the speed of light. Orders of magnitude are obtained through this classical approach, and are compared to the General Relativity results.Saclay T03/171