Spinning compact objects in extreme-mass-ratio inspirals

Since the first landmark observation of gravitational waves (GWs) in 2015, GW astronomy has tremendously impacted fundamental physics and astrophysics. A network of four ground-based detectors (the two LIGOs, Virgo and KAGRA) is now in operation, routinely detecting new events. Future space-based obser- vatories, like the Laser Interferometer Space Antenna (LISA), hold the promise to revolutionize GW astronomy by detecting sources non-observable by current detectors, opening avenues for groundbreaking discoveries. Among the prime targets of LISA are extreme mass ratio inspirals (EMRIs), which are binaries consisting of a stellar-mass compact object slowly inspiraling into a supermassive black hole. These systems are unique probes of astrophysics and fundamental physics. Motivated by their potential, here we study in detail the EMRI dynamics in the presence of a spinning small compact object. The tiny mass-ratio in EMRI binaries allows us to treat the smaller companion as a point particle endowed with mass and spin. The latter are free parameters independent of the internal structure of the infalling compact object. The radiation-reaction forces (known as self-force) and equations of motion are typically modeled with perturbative approaches in the mass ratio. At leading order, the dynamics of the particle is governed by the adiabatic emission of energy and angular momentum in gravitational radiation, causing the secular decay of the orbits. All subleading corrections to this general picture are called post-adiabatic terms. The spin of the small compact object starts affecting the GW phase at the first post-adiabatic order (as does the first-order conservative and second-order dissipative self-force). In this thesis, we focus on the measurability of the smaller companion spin by an EMRI detection with LISA. Using the Teukolsky formalism, we derive the GW fluxes and the adiabatic orbital evolution for a spinning particle in the case of circular, equatorial orbits with (anti-)aligned spins. We provide the spin-induced corrections to GW fluxes (numerically and semi-analytically), along with the corresponding post-adiabatic effects on the GW phase, which are novel results for a Kerr background. Based on the phase difference between the gravitational signal from a spinning and a non-spinning particle, we develop a criterion to determine the minimum value of the spin resolvable by LISA. Our analysis points out that precise, model-independent tests on the nature of the small compact object could be achieved by measuring its intrinsic angular momentum. We also suggest that LISA could test the so-called Kerr bound that limits the maximum spin of a rotating black hole, allowing for theory-agnostic constraints. We then perform an accurate Fisher-matrix study of the EMRI parameters using Teukolsky waveforms to leading order in an adiabatic expansion on a Kerr background. Our parameter estimation takes into account the motion of the LISA constellation, higher harmonics, and includes the leading correction from the smaller companion spin in the post-adiabatic approximation. We particularly focus on the measurability of the small body spin, showing that, for spin-aligned EMRIs on quasi-circular orbits, it cannot be measured with sufficient accuracy. However, due to correlations, its inclusion in the waveform model can deteriorate the accuracy on the measurements of other parameters by orders of magnitude, unless a physically-motivated prior on the small compact object spin is imposed.