Probing Fundamental Physics via black hole perturbation theory: ringdown and extreme mass ratio inspirals in and beyond-vacuum General Relativity

Since the first gravitational-wave detection (GW150914) by LIGO in 2015, significant developments have been made in gravitational wave experimental science. In this decade, not only have Virgo and KAGRA joined LIGO to form an interferometer network, but the sensitivity of each detector has been increased, making gravitational-wave physics increasingly a precision science. As a result of these improvements, LIGO-Virgo-KAGRA network has recently detected GW250114, the binary black hole coalescence with the highest signal-to-noise ratio to date. The planned upgrades for forthcoming O5 observing run, and next-generation observatories, such as the Einstein Telescope, Cosmic Explorer, and the space-based Laser Interferometer Space Antenna (LISA) mission, will usher in the era of precision gravity. Gravitational waves will increasingly be used to address open problems in fundamental physics, such as testing General Relativity, probing the nature of dark matter and the behaviour of matter at supranuclear densities, and studying the astrophysical environments in which black holes reside. Both the ringdown, the last part of the waveform from any binary coalescence, and extreme mass ratio inspirals, among the target sources of LISA, are particularly sensitive to beyond-vacuum General Relativity effects, and can both be accurately described by black hole perturbation theory. A consistent fully-relativistic investigation of the impact of beyond-General Relativity and environmental effects has been started recently and several questions remained unanswered. In this context, scalar fields are particularly interesting because they can play a dual role: they can act both as dark-matter candidates and as extra gravitational degrees of freedom. A first investigation proved that scalar fields may leave detectable imprints in both ringdown and extreme mass-ratio inspiral waveforms. Encouraged by these results, we describe the theoretical framework to numerically evolve extreme mass ratio inspiral in a large class of beyond-General Relativity theories, all featuring an extra scalar degree of freedom coupled to the metric in the gravitational sector. After building up a consistent framework to compute scalar fluxes emitted by generic extreme-mass ratio inspirals, we focus on the case of inclined configurations. We show that the orbital inclination can help to detect the imprint of an extra degree of freedom. We also explore the detectability of gravitational atoms via extreme mass-ratio inspirals and ringdown. Gravitational atoms are compact objects composed of a metastable scalar cloud bound to a black hole. They are well-suited to describe dark-matter halos around black holes. Complementary to previous studies, which showed that LISA may distinguish gravitational atoms from supermassive black holes as primary components of extreme mass-ratio inspirals, we investigate the opposite configuration in which a stellar-mass gravitational atom orbits around a supermassive black hole. We show that, when the secondary is a black hole, detected waveforms are unchanged with respect to the vacuum case, rendering this channel unpromising for detection. The observability of gravitational atoms via the ringdown is, instead, promising: an inspection of gravitational atom spectroscopy reveals that they may be detectable even with current interferometers if the scalar cloud is compact enough. Finally, we discuss the excitation of quasi-normal modes in pure vacuum General Relativity. Quasi-normal modes are a central feature in ringdown modelling. They characterize the frequency-domain spectrum of the gravitational wave signal emitted by the oscillating post-merger remnant. Exploiting the point-particle approximation, we model the astrophysical excitation of quasi-normal modes by a plunging particle from the innermost circular orbit. Extending previous results towards a deeper understanding of the ringdown, we pave the way for further investigation of not-yet clear aspects of the ringdown.