| dc.description.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. | |
