  In this work, we use the framework of effective field theory to couple
Einstein's gravity to quantum electrodynamics (QED) and determine the
gravitational corrections to the two-loop beta function of the electric charge
in arbitrary electrodynamics (Lorentz-like) and arbitrary (de Donder like)
gravitational gauges. Our results indicate that gravitational corrections do
not alter the running behavior of the electric charge; on the contrary, we
observe that it gives a positive contribution to the beta function, making the
electric charge grow even faster.
