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’.

Solitonic boson stars are stable objects made of a complex scalar field with a compactness that can reach values comparable to that of neutron stars. A recent study of the collision of identical boson stars produced only non-rotating boson stars or black holes, suggesting that rotating boson stars may not form from binary mergers. Here we extend this study to include an analysis of the gravitational waves radiated during the coalescence of such a binary, which is crucial to distinguish these events from other binaries with LIGO and Virgo observations. Our studies reveal that the remnant's gravitational wave signature is mainly governed by its fundamental frequency as it settles down to a non-rotating boson star, emitting significant gravitational radiation during this postmerger state. We calculate how the waveforms and their post-merger frequencies depend on the compactness of the initial boson stars and estimate analytically the amount of energy radiated after the merger.

Boson stars, self-gravitating objects made of a complex scalar field, have been proposed as simple models for very different scenarios, ranging from galaxy dark matter to black hole mimickers. Here we focus on a very compact type of boson stars to study binary mergers by varying different parameters, namely the phase shift, the direction of rotation and the angular momentum. Our aim is to investigate the properties of the object resulting from the merger in these different scenarios by means of numerical evolutions. These simulations, performed by using a modification of the covariant conformal Z4 (CCZ4) formalism of the Einstein Equations that does not require the algebraic enforcing of any constraint, indicate that the final state after a head-on collision of low mass boson stars is another boson star. However, almost complete annihilation of the stars occurs during the merger of a bosonantiboson pair. The merger of orbiting boson stars form a rotating bar that quickly relaxes to a non-rotating boson star.