Gravitational Moller scattering, Lorentz violation and finite temperature

A formal analogy between the gravitational and the electromagnetic fields leads to the notion of Gravitoelectromagnetism (GEM) to describe gravitation. A Lagrangian formulation for GEM is developed for scattering processes with gravitons as an intermediate state, in addition to photons for electromagnetic scattering. The differential cross section is calculated for gravitational Moller scattering based on GEM theory. This gravitational cross section is obtained for cases where the Lorentz symmetry is maintained or violated. The Lorentz violation is introduced with the non-minimal coupling term. In addition, using the Thermo Field Dynamics formalism, thermal corrections to the differential cross section are investigated. By comparing the electromagnetic and GEM versions, of Moller scattering, it is shown that the gravitational effect may be measured at an appropriate energy scale.