Gravitational Lensing Formalism

In general relativity, a point mass deflects a light ray with impact parameter ${\displaystyle b~}$ by an angle approximately equal to

${\displaystyle {\hat {\alpha }}={\frac {4GM}{c^{2}b}}}$

where G is the gravitational constant, M the mass of the deflecting object and c the speed of light. A naive application of Newtonian gravity can yield exactly half this value, where the light ray is assumed as a massed particle and scattered by the gravitational potential well. This approximation is good when ${\displaystyle 4GM/c^{2}b}$ is small.

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