Gravitational waves from extreme mass ratio inspirals in Kerr-MOG spacetimes

Abstract This work elaborates on a detailed analysis of the novel characteristics of gravitational waves (GWs) generated by extreme mass-ratio inspirals (EMRIs) within the framework of modified gravity (MOG). Our study begins by exploring the geometrical and dynamical properties of the Kerr-MOG spacetime. We employ the numerical kludge (NK) method for waveform simulations and reveal that the parameter α , representing deviations from general relativity (GR), significantly impacts the frequencies of geodesic orbits and, consequently, the EMRI waveforms. However, the waveform confusion problem remains mainly unresolved, posing a challenge in distinguishing between the underlying gravitational theories based on the observed EMRI waveforms. Notably, by incorporating the effects of radiation reaction and increasing the MOG parameter α , we observe a substantial reduction in the waveform overlap over time. This reduction could enhance our ability to discern between different waveforms over an extended period. Our analysis further identifies that α begins to influence energy fluxes at the 1 post-Newtonian (PN) order, highlighting its leading-order effects on the orbital dynamics. Additionally, we find that α becomes detectable when the estimated overlap crosses the detection threshold by computing the mismatch. And we estimate that the detection error for α can be constrained to Δ α ≈ 1.85 × 10 -4 by using the Fisher information matrix (FIM) method, demonstrating the potential of space-based gravitational wave detectors to probe deviations from GR with high precision.