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Oh leave the Wise our measures to collate, One thing at least is certain, light has weight, One thing is certain and the rest debate, Light rays, when near the Sun, do not go straight. - Arthur Stanley Eddington, RAS dinner
A massive body, like a galaxy cluster, can cause enough curvature in spacetime for a beam of light, which would otherwise hit the body, to bend around the cluster and travel without being hit. This phenomenon, predicted by Einstein’s General Theory of Relativity(GTR), is called Gravitational Lensing. Consequently, we may see the light emerging from a source of light lying behind the massive body in our line of sight. In this case, the massive body is known as a gravitational lens.
Gravitational Lensing is a consequence of Einstein's General Theory of Relativity, but even before this theory was formulated, there were ideas that gravity could influence light.
Let us treat light as a particle, and assume it behaves like a massive body in a Newtonian gravitational field generated by a mass, like a star or a galaxy. We can then calculate the angle by which a light beam arriving towards the mass from infinity will be deflected. J. Soldner (1804) ((translation of Soldner’s paper is provided by Jaki (1978))), a Munich astronomer calculated this deflection angle $\alpha$ as:
where G is the gravitational constant, M is the mass of the massive body, v is the velocity of light, and r is the impact parameter, as shown in the following figure.
Schematic diagram to illustrate the deflection of particles around a massive body. Image produced by the author.
For very small angles, $\alpha = \frac{2GM}{v^2 r}$. Note that there is no term for the mass of the photon. Hence, even Newtonian gravity, with the treatment of light like a point mass, predicts the deflection light around massive objects.
Einstein’s rough calculations of Gravitational Lensing in 1912. Credits - Collected Papers of Albert Einstein, Vol. 3, p. 585
In 1911, Einstein published a paper that predicted the same deflection as predicted by Newtonian theory(1911) and calculated the deflection of light rays coming from a star that lies just at the limb of the sun. It is possible to detect this deflection during a solar eclipse, since most of the light from the sun is blocked by the moon, and hence it becomes possible to see the stars around the edge of the sun.
It was later realized by Einstein when he developed his theory of gravity, that his calculations were wrong by a factor of two. The correct formula for the deflection of light is given by: