Bending of Light in Quantum Gravity

Abstract

We consider the scattering of lightlike matter in the presence of a heavy scalar object (such as the Sun or a Schwarzschild black hole). By treating general relativity as an effective field theory we directly compute the nonanalytic components of the one-loop gravitational amplitude for the scattering of massless scalars or photons from an external massive scalar field. These results allow a semiclassical computation of the bending angle for light rays grazing the Sun, including long-range $\hslash$ contributions. We discuss implications of this computation, in particular the violation of some classical formulations of the equivalence principle.

Comments: 5 pages, 1 figure, v2: typos corrected, version to be published in PRL, v3: signs corrected