[eng] The aim of this project is to present the current state of Neutron Star-Black
Hole system detections and give a sense of how they can be studied and what can
be learned from them. For that, it walks the reader through the basics of General
Relativity and Gravitational Waves theory, with an overview of linearized theory,
the wave solutions of the Einstein Equations and the quadrupole approximation.
Then, the physics of the formation and composition of the sources that radiate
gravitational waves are explained in order to show how they a ect the emitted ra-
diation. Namely, these sources are black holes, neutron stars and white dwarfs in
binary systems, and detecting and understanding their e ects on the gravitational
wave radiation would help to better comprehend them and allow the inference of
their equation of state. In addition, it describes the process of detection and sub-
sequent data analysis and reviews the models utilized to characterize gravitational
waveforms using analytical and numerical solutions. This leads to the discussion
of the gravitational-wave signals detected so far, speci cally the only two Neutron
Star-Black Hole detections to date. Finally, a comparison of the agreement between
di erent waveform models is used to better understand their reliability and the sig-
ni cance of possible systematic errors in terms of the current and future sensitivity
of gravitational wave detectors.