  Lorentz symmetry is a fundamental symmetry in the Standard Model (SM) and in
General Relativity (GR). This symmetry holds true for all models at low
energies. However at energies near the Planck scale, it is conjectured that
there may be a very small violation of Lorentz symmetry. The Standard Model
Extension (SME) is a quantum field theory that includes a systematic
description of Lorentz symmetry violations in all sectors of particle physics
and gravity. In this paper SME is considered to study the physical process of
Bhabha Scattering in the Gravitoelectromagnetism (GEM) theory. GEM is an
important formalism that is valid in a suitable approximation of general
relativity. A new non-minimal coupling term that violates Lorentz symmetry is
used in this paper. Differential cross section for gravitational Bhabha
scattering is calculated. The Lorentz violation contributions to this GEM
scattering cross section are small and are similar in magnitude to the case of
the electromagnetic field.
