Extreme mass-ratio inspirals and extra dimensions: Insights from modified Teukolsky framework

Extreme mass-ratio inspirals (EMRIs) offer a promising avenue to test extra-dimensional physics through gravitational wave (GW) observations. In this work, we study equatorial eccentric EMRIs around a spherically symmetric braneworld black hole, focusing on the influence of a tidal charge parameter arising from extra dimensions. Using the fact of tr-symmetry of the spacetime under consideration, we implement the Modified Teukolsky Equation (MTE) framework, incorporating the non-Ricci-flat nature of the spacetime. We compute the relevant observables and perform a comparative analysis with the results obtained from the Dudley-Finley (DF) approximation. Our findings indicate that the constraint on the tidal charge remains nearly the same in both approaches MTE and DF thus supporting previous studies on EMRIs in braneworld scenarios within the DF approximation. Furthermore, the difference in the mismatch between the two formulations exhibits deviations as the orbital eccentricity increases. Therefore, these findings highlight not only the observational potential of future low-frequency detectors like the Laser Interferometer Space Antenna (LISA) but also bring out the effectiveness of the DF approximation as well as the importance of the MTE framework for accurately modeling binaries in theories beyond GR.