The grand challenges of contemporary fundamental physics—dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem—all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on ‘Black holes, Gravitational waves and Fundamental Physics’.

Ultralight scalars have been predicted in a variety of scenarios, and advocated as a possible component of dark matter. These fields can form compact regular structures known as boson stars, or---in the presence of horizons---give rise to nontrivial time-dependent scalar hair and a stationary geometry. Because these fields can be coherent over large spatial extents, their interaction with "regular" matter can lead to very peculiar effects, most notably resonances. Here we study the motion of stars in a background describing black holes surrounded by non-axially symmetric scalar field profiles. By analyzing the system in a weak-field approach, we find that the presence of a scalar field gives rise to secular effects akin to ones existing in planetary and accretion disks. Particularly, the existence of resonances between the orbiting stars and the scalar field may enable angular momentum exchange between them, providing mechanisms similar to planetary migration. Additionally, these mechanisms may allow \textit{floating orbits}, which are stable radiating orbits. We also show, in the full relativistic case, that these effects also appear when there is a direct coupling between the scalar field and the stellar matter, which can arise due to the presence of a scalar core in the star or in alternative theories of gravity.Comment: 21 pages, 13 figures. Accepted for publication in Physical Review D, comments are welcom

We consider motion in spherically symmetric but time-dependent backgrounds. This problem is of interest, for example, in the context of ultralight dark matter, where galactic haloes produce a time-dependent and periodic gravitational potential. We study the properties of motion of stars in such spacetimes, for different field strengths and frequency, and including dissipative effects. We show that orbital resonances may occur and that spectroscopic emission lines from stars in these geometries exhibit characteristic, periodic modulation patterns. In addition, we work out a fully relativistic and weak-field description of a special class of time-periodic geometries, that of scalar oscillatons. When applied to the galactic center, our results indicate that the motion of S2-like stars may carry distinguishable observational imprints of ultra-light dark matter. CONTENTS

Precise measurements of the S-stars orbiting SgrA* have set strong constraints on the nature of the compact object at the centre of the Milky Way. The presence of a black hole in that region is well established, but its neighbouring environment is still an open debate. In that respect, the existence of dark matter in that central region may be detectable due to its strong signatures on the orbits of stars: the main effect is a Newtonian precession which will affect the overall pericentre shift of S2, the latter being a target measurement of the GRAVITY instrument. The exact nature of this dark matter (e.g. stellar dark remnants or diffuse dark matter) is unknown. This article assumes it to be a scalar field of toroidal distribution, associated with ultralight dark matter particles, surrounding the Kerr black hole. Such a field is a form of ‘hair’ expected in the context of superradiance, a mechanism that extracts rotational energy from the black hole. Orbital signatures for the S2 star are computed and shown to be detectable by GRAVITY. The scalar field can be constrained because the variation of orbital elements depends both on the relative mass of the scalar field to the black hole and on the field mass coupling parameter.

Low-energy, self-gravitating solutions of a scalar field coupled to gravity, described by the Schrodinger-Poisson system, are good candidates for realistic astrophysical structures, being particularly suited to describe dark matter halos. In this work we study the scenario in which one of these structures is gravitationally perturbed by a point-like mass. We analyse the effects that the body has on the distribution of the scalar field and how it backreacts on the body's motion. We show that an initially static, spherical structure can develop rotating non-spherical clumps, the amplitude and the velocity of which are directly related to the mass of the orbiting particle. We also study the dissipation mechanisms involved in the transit of the point-like particle across the scalar field structure and we observe that the force responsible for the dissipation scales as the square of the mass of the particle. CONTENTS