Extreme Mass Ratio Inspirals in rotating Dark Matter Spike

Gravitational wave (GW) signals from extreme mass ratio inspirals (EMRIs) are a key observational

target for the Laser Interferometer Space Antenna (LISA). The waveforms may be affected by

the astrophysical environment surrounding the central black hole (BH), and in particular by the

surrounding dark matter (DM) distribution. In this work, we consider the effect of a rotating DM

“spike” around a central Kerr BH, and assess its detectability with LISA. Using a fully relativistic

model for the rotating spike, we investigate its effect on the inspiral and hence on the emitted GW

signals. We compute dephasings and mismatches to quantify how the spin of the primary BH affects

the binary dynamics and the gravitational waveform. We show that the modifications due to the spin

of the primary BH improve the detection prospects of DM spikes with LISA, and must be taken into

account for future parameter estimation studies.