Lorentz Symmetry Breaking as a Nonlinear ODE

In this presentation, I go over a vector model of Lorentz symmetry breaking coupled to the bumblebee model of gravity, where the vector field does not lie at a minimum. Using a modified electrodynamics model paired with a nonlinear interaction term, I study the flat spacetime solutions in the form of an ordinary second order nonlinear differential equation. The nonlinear interaction term takes the form of a quadratic term or that of the Kummer Confluent Hypergeometric function. With the flat spacetime solutions’ various forms found through substitutions, and a knowledge of other known and solved differential equations and techniques, I investigate the behavior of the equation both analytically and numerically.