  The Fradkin-Schwinger functional methods to represent a Green function in an
external gravitational field are used to study the eikonal and the
next-to-eikonal limit, including the nonlinear gravitational interactions, of
the scattering amplitudes of an ultra-relativistic scalar particle on a static
super-massive scalar target in the nearly forward limit. The functional
approach confirms the exponentiation of the leading eikonal which also applies
to the first non-leading power in the energy of the light particle, moreover
includes the interaction at impact parameter much larger than the Schwarzschild
radius associated with the center of mass energy in the ultra-relativistic
limit.
