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’.

We perform numerical evolutions of the fully nonlinear Einstein (complex, massive) Klein-Gordon and Einstein (complex) Proca systems, to assess the formation and stability of spinning bosonic stars. In the scalar (vector) case these are known as boson (Proca) stars. Firstly, we consider the formation scenario. Starting with constraint-obeying initial data, describing a dilute, axisymmetric cloud of spinning scalar or Proca field, gravitational collapse toward a spinning star occurs, via gravitational cooling. In the scalar case the formation is transient, even for a nonperturbed initial cloud; a nonaxisymmetric instability always develops ejecting all the angular momentum from the scalar star. In the Proca case, by contrast, no instability is observed and the evolutions are compatible with the formation of a spinning Proca star. Secondly, we address the stability of an existing star, a stationary solution of the field equations. In the scalar case, a nonaxisymmetric perturbation develops, collapsing the star to a spinning black hole. No such instability is found in the Proca case, where the star survives large amplitude perturbations; moreover, some excited Proca stars decay to, and remain as, fundamental states. Our analysis suggests bosonic stars have different stability properties in the scalar (vector) case, which we tentatively relate to its toroidal (spheroidal) morphology. A parallelism with instabilities of spinning fluid stars is briefly discussed.

Spherically symmetric bosonic stars are one of the few examples of gravitating solitons that are known to form dynamically, via a classical process of (incomplete) gravitational collapse. As stationary solutions of the Einstein–Klein-Gordon or the Einstein–Proca theory, bosonic stars may also become sufficiently compact to develop light rings and hence mimic, in principle, gravitational-wave observational signatures of black holes (BHs). In this paper, we discuss how these horizonless ultracompact objects (UCOs) are actually distinct from BHs, both phenomenologically and dynamically. In the electromagnetic channel, the light ring associated phenomenology reveals remarkable lensing patterns, quite distinct from a standard BH shadow, with an infinite number of Einstein rings accumulating in the vicinity of the light ring, both inside and outside the latter. The strong lensing region, moreover, can be considerably smaller than the shadow of a BH with a comparable mass. Dynamically, we investigate the fate of such UCOs under perturbations, via fully nonlinear numerical simulations and observe that, in all cases, they decay into a Schwarzschild BH within a time scale of $\mathcal{O}(M)$, where $M$ is the mass of the bosonic star. Both these studies reinforce how difficult it is for horizonless UCOs to mimic BH phenomenology and dynamics, in all its aspects.

Physics beyond the standard model is an important candidate for dark matter, and an interesting testing ground for strong-field gravity: the equivalence principle ‘forces’ all forms of matter to fall in the same way, and it is therefore natural to look for imprints of these fields in regions with strong gravitational fields, such as compact stars or black holes (BHs). Here we study general relativity minimally coupled to a massive vector field, and how BHs in this theory lose ‘hair’. Our results indicate that BHs can sustain Proca field condensates for extremely long time-scales.