Extreme mass-ratio inspiral as a probe of extra dimensions: The case of spinning massive object

Extreme mass-ratio inspiral (EMRI), as one of most important and promising gravitational wave (GW) sources, which is the ideal tool to test fundamental theories and nature of massive black hole (MBH). In this paper, we consider the EMRI system consisting of a rotating barneworld MBH with tidal charge Q and a stellar-mass compact object (CO), where a non-spinning CO inspirals on the equatorial and circular orbits around the MBH. Under the adiabatic approximate condition, we show the evolution of circular orbital radius by computing the EMRI fluxes and orbital phase modified by tidal charge. We find that the positive and negative values of tidal charges have the difference influences on the EMRI orbital dynamics. In particular, the inspiral motion of CO in the rotating barneworld MBH with a negative tidal charge would be end more earlier than the positive tidal charge case. Accordingly, the EMRI waveforms from the positive tidal charge cases can put more rigorous constraint results comparing with the negative tidal charge cases. Finally, we analyse the phase differences of two EMRI waveforms from Kerr BH and rotating braneworld BH with tidal charge by computing dephasing and mismatch. Our results indicate that LISA can distinguish the EMRI waveforms from rotating braneworld BH with the negative tidal charge as smaller as Qmin∼−10−6 under the suitable scenarios, which can sever as the unique discriminator of detecting the physics of extra dimensions.