SEMICLASSICAL VIOLATION of THE EQUIVALENCE PRINCIPLE IN THE GRAVITATIONAL LENSES REALM

Abstract

An expression for the gravitational deflection angle of a high-energy massless scalar boson is computed using the JWKB method. The resulting expression depends on the energy of the scalar boson or, equivalently, on its wavelength, even to first order in GM/b, where G is Newton's constant, M is the mass of the gravitational source, and b is the impact parameter. on the other hand, combining the expressions for the magnification of two images obtained from a gravitational lens with the classical expression for the cross section, it is found that for purely gravitational scatterings the gravitational cross sections are proportional to the relative intensities. As a consequence of this remarkable proportionality and of the fact that the deflection angle obtained via the JWKB method is energy dependent, we come to the conclusion that chromatic effects in the gravitational lenses at the semiclassical level are possible, which violates the classical equivalence principle. The probability of detecting this tiny effect in the foreseeable future is discussed.