Black Hole Solutions in Modified Gravity and Lorentz Symmetry Breaking as a Nonlinear ODE

The current best theory of gravity in the universe is called General Relativity, first conceived in 1915 by Einstein. It describes gravity as the effect of curved space and time around massive objects like stars and black holes. The possibility that some fundamental principles of General Relativity can break at miniscule scales has been frequently explored, including the concept of "Lorentz Symmetry". The motivation of this research is to explore some possibilities that Lorentz Symmetry breaking potentials could take the form of, and how that changes our current model of physics. Using a modified electrodynamics model paired with a nonlinear interaction term, we 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, we investigate the behavior of the equation both analytically and numerically, and draw conclusions about its behavior over large distances. *Modified misspelled in title "Black Hole Solutions in Mdified Gravity and Lorentz Symmetry Breaking as a Nonlinear ODE"