Lyapunov Exponents in Modified Gravity

Light-rings are key targets for near-future space-based VLBI missions. The ratio of flux measured between successive light-rings is characterized by the Lyapunov exponents of the corresponding nearly-bound null geodesics. Therefore, understanding Lyapunov exponents in this environment is of crucial importance to understanding black hole observations in general, and in particular, they offer a route for constraining modified theories of gravity. While recent work has made significant progress in describing these geodesics for Kerr, a theory-agnostic description is complicated by the fact that Lyapunov exponents are time-parameterization dependent, which necessitates care when comparing the Lyapunov exponents of null geodesics in two different theories. In this work, we present a numerical framework for comparing the Lyapunov exponents of null geodesics in Kerr with those in arbitrarily modified theories, and then present the results of calculating the Lyapunov exponents for null geodesics in two particular effective theories, sGB and dCS.