Gravitational wave from extreme mass-ratio inspirals around a Kerr–Taub–NUT black hole

Abstract

We have computed the gravitational waves emitted from extreme mass-ratio inspirals (EMRIs) around the Kerr–Taub–NUT black hole using a hybrid method. Firstly, we derive the analytic expressions of the orbital energy, angular momentum and Carter constant for the generic geodesic orbits, and compute the orbital frequencies numerically. To evolve the orbital parameters adiabatically, we adopt the hybrid fluxes based on the radial motion period in the Kerr–Taub–NUT black hole and the Kerr fluxes in the numerical kludge model. Using the inspiraling trajectories, we compute EMRI waveform to assess the difference of waveforms from the Kerr and Kerr–Taub–NUT BHs. We find that, LISA can distinguish the EMRIs waveform from the Kerr–Taub–NUT black hole with a NUT charge as smaller as $N_{\text{min}}\sim 10^{-6}$. After one year observation of EMRI signal, the constraint on NUT charge by LISA can be measured within an error of $\Delta N\sim 10^{-6}$, which is correlated with the measurement errors of the other intrinsic parameters.