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 as extra dimensions. Using the fact of tr-symmetry of the spacetime under consideration, we implement the Modified Teukolsky Equation (MTE) framework and compute observables, as well as compare the results with those from the standard Teukolsky formalism for general relativity (GR). Our analysis reveals significant deviations in dephasing and mismatch values, especially for the higher eccentricities. These findings highlight not only the observational potential of future low-frequency detectors like the Laser Interferometer Space Antenna (LISA) but also the necessity of using the MTE framework for accurately modeling binaries in theories beyond GR.