• black hole
• extreme mass ratio inspirals
• faithfulness
• gravitational waves
• inspiral dynamics
• laser interferometer space antenna
• neutron star
• scalar-tensor theories
• waveform modeling

This thesis focuses on the study of signal emission from compact binary systems known
as Extreme Mass Ratio Inspirals (EMRIs). These are asymmetric binaries composed of
a stellar-mass compact object orbiting around a much heavier black hole of 10^(5) – 10^(9)
solar masses. Such systems are expected to complete about 10^(4) – 10^(5) orbital cycles
in the sensitivity band of the Laser Interferometer Space Antenna (LISA), which is a
future space-based gravitational wave observatory with a launch date programmed in
2037. Thus, in just over a decade, we may be able to observe gravitational wave signals
from EMRIs. They are promising target laboratories to test General Relativity or its
possible deviations in the strong-field regime, since several thousand orbital cycles are
likely to be completed in the region near the massive black hole’s horizon. In this thesis, I
study these sources within a scalar-tensor framework where a real massless scalar field is
non-minimally coupled to the metric tensor. The presence of an additional scalar degree of
freedom in the gravitational sector affects the radiation emission with an extra channel for
energy and angular momentum dissipation. Consequently, the orbital dynamics and the
evolution of the gravitational wave frequency are modified, leaving a detectable imprint
on the emitted waveform. The working theoretical assumptions made in this thesis lead
to a decoupling between the scalar field and the metric equations. The non-minimal
coupling between these two fields is encoded in a dimensionless parameter, called scalar
charge, which quantifies the interaction strength between the secondary compact object
and the scalar field. In this work, we do not assume a specific scalar-tensor theory and
treat the scalar charge as a free phenomenological parameter. This approach can be
applied to a wide range of scalar-tensor theories of gravity, in which the background
spacetime generated by the massive black hole can be described by the Kerr solution of
Einstein’s equations, neglecting any effect of the scalar field. Furthermore, the large mass
ratio between the primary and secondary bodies allows us to solve the field equations
perturbatively. At first order in the mass ratio, the scalar perturbation equation is a
wave equation with a source term determined by the secondary object. Recently, this
system has been studied for EMRIs in which the smaller body is a black hole. In this
thesis, instead, we focus on the case in which it is a scalarized neutron star on equatorial
circular orbits around a spinning massive black hole. Firstly, we compute the scalar and
the gravitational energy fluxes emitted by solving the perturbation equations in a Kerr
background. Then, these fluxes are used to determine the orbital evolution of the final year
before the plunge, and to reconstruct the waveform of the signal emitted in the last stages
of the inspiral phase. This analysis is conducted for six different binary configurations,
varying the masses of the black hole and the neutron star, to explore different regions
of the LISA sensitivity band. Finally, we carry out a signal analysis in our framework
to identify potential observational imprints of the scalarization, independently of the
specific underlying theory. More precisely, we compare the waveforms emitted by the
EMRI systems with and without scalar charge, using tools such as the faithfulness and
the signal-to-noise ratio, evaluated for different luminosity distances. This allows us to
determine the minimum detectable scalar charge for the various binary configurations
under consideration.