From Relativity to Beyond: Orbital Shifts in Extreme Mass Ratio Inspirals under Modified Gravity

Abstract

General Relativity has revolutionized our understanding of gravity, yet chal lenges remain. Its incompatibility with quantum mechanics and the unresolved nature of singularities in high-density regimes highlight the need for modifica tions. These modifications might manifest in the strong-gravity domain of black holes and compact objects or become relevant only at Planck-scale phenomena. Gravitational waves provide a unique opportunity to test modified gravity theo ries in the strong-gravity regime, especially with next-generation high-precision detectors. However, detecting these effects requires robust theoretical models, beginning with an understanding of how black hole binaries evolve in modified gravity theories. This thesis investigates extreme mass ratio inspirals, systems in which a stellar-mass object orbits a supermassive black hole. These inspirals evolve over long timescales, allowing cumulative deviations from General Relativity to emerge. Two modified gravity theories, dynamical Chern-Simons (dCS) and scalar Gauss-Bonnet (sGB), are explored. A geometric framework for dynamical systems is introduced to analyze resonances, which are especially sensitive to per turbations. Additionally, an effective potential approach is employed to examine phase-space regions of bound orbits in extreme mass ratio binaries. We found that dCS enlarges the region of bound orbits aligned with the spin of the super massive black hole and shifts all orbits inward. In contrast, sGB increases the regions of bound orbits both aligned and counter-aligned with the spin, while shifting all orbits outward. These findings suggest trends in orbital dynamics that could inform future observational tests of modified gravity theories.