EMRIs around j=1 black holes with synchronised hair

We study extreme mass ratio inspirals (EMRIs) due to an infalling Light Compact Object (LCO) onto a generic class of stationary and axi-symmetric massive compact objects (MCO - with or without a horizon). Using the quadrupole hybrid formalism we obtain a master formula for the evolution of the radius of the LCO and find qualitatively different behaviours depending on the geodesic structure of the MCO. We then specialize the MCO to a black hole with synchronised scalar hair (BHsSH). To allow a comparison with a highly spinning Kerr BH, we consider BHsSH with dimensionless spin, j = 1. This yields two distinct sequences of solutions. The first harbours Kerr-like solutions with maximal hairiness of similar to 10%. The corresponding EMRIs are Kerr-like, but the cut-off frequency can be a few times smaller than in Kerr, yielding waveforms with quantitatively significant non-Kerrness. The second sequence links the extremal Kerr black hole to a mini-boson star with j = 1. Here we observe qualitative non-Kerrness, such as the non-monotonically increase of the angular velocity and stagnation endpoints, reflecting Kerr-unlike geodesic structures.

Automated summary

In this study, we investigate extreme mass ratio inspirals (EMRIs) caused by the infalling of a Light Compact Object (LCO) onto a generic class of stationary and axi-symmetric massive compact objects (MCO - with or without a horizon). By using the quadrupole hybrid formalism, we derive a master formula for the evolution of the LCO radius and observe qualitatively different behaviors depending on the geodesic structure of the MCO. We then focus on a special case of MCO, a black hole with synchronised scalar hair (BHsSH), and compare it with a highly spinning Kerr BH, revealing significant non-Kerrness in the waveforms.