3 research outputs found
Neutrino and photon lensing by black holes: radiative lens equations and post-Newtonian contributions
We extend a previous phenomenological analysis of photon lensing in an
external gravitational background to the case of a massless neutrino, and
propose a method to incorporate radiative effects in the classical lens
equations of neutrinos and photons. The study is performed for a Schwarzschild
metric, generated by a point-like source, and expanded in the Newtonian
potential at first order. We use a semiclassical approach, where the
perturbative corrections to neutrino scattering, evaluated at one-loop in the
Standard Model, are compared with the Einstein formula for the deflection using
an impact parameter formulation. For this purpose, we use the renormalized
expression of the graviton/fermion/fermion vertex presented in previous
studies. We show the agreement between the classical and the semiclassical
formulations, for values of the impact parameter of the neutrinos of the
order of , measured in units of the Schwarzschild radius. The
analysis is then extended with the inclusion of the post Newtonian corrections
in the external gravity field, showing that this extension finds application in
the case of the scattering of a neutrino/photon off a primordial black hole.
The energy dependence of the deflection, generated by the quantum corrections,
is then combined with the standard formulation of the classical lens equations.
We illustrate our approach by detailed numerical studies, using as a reference
both the thin lens and the nonlinear Virbhadra-Ellis lens