LISA -- Laser Interferometer Space Antenna -- will be launched in 2035 and will observe gravitational wave (GW) sources in the frequency range 0.1-100 mHz. Extreme mass ratio inspirals (EMRIs) are one of the prime sources for LISA. As a result of N-body interaction of stellar remnants in the galactic nuclei, a compact object, (CO), (a stellar mass black hole or a neutron star) could be thrown into a very eccentric orbit passing near a massive black hole (MBH). The GWs bursts emitted at each periapse passage near the MBH shrink the orbit and reduce its eccentricity, until the CO decouples from the stellar environment and forms a two-body system with an extreme mass ratio: EMRI. 

In this project, we will deal with "dirty" EMRIs, those are the systems where an external perturber plays an important role. (1) Gas as an external perturber. The interaction of a CO orbiting MBH with accretion disk in active galactic nuclei is the most plausible explanation for the quasi-periodic eruptions observed in X-rays. In this project, we propose combined GW observations of EMRIs with LISA and archival search for X-ray bursts to support this hypothesis. (2) Nuclear stellar cluster as an external perturber. We will consider the interaction of a CO with the stellar environment in galactic nuclei to reduce uncertainties in the EMRI event rate. (3) Dark matter as an external perturber.  Dark matter could form around an MBH through super-radiant instability or segregate around an MBH from the remnant of cosmological evolution. Furthermore, dark matter may exhibit a very steep density profile (known as a dark matter spike), which can affect the dynamics of EMRIs via dynamical friction. We will investigate the possibility of detecting dark matter through GW observations of EMRIs with LISA.

The primary tool connecting all the objectives mentioned above is the development of forced geodesic motion around a Kerr black hole, which will be developed using the osculating elements approach in its relativistic representation.