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’.

There have been increasing theoretical speculations and observational indications that certain globular clusters (GCs) could contain a sizeable population of stellar mass black holes (BHs). In this paper, we shortlist at least 29 Galactic GCs that could be hosting a subsystem of BHs (BHS). In a companion paper, we analysed results from a wide array of GC models (simulated with the MOCCA code for cluster simulations) that retained few tens to several hundreds of BHs at 12 Gyr and showed that the properties of the BHS in those GCs correlate with the GC's observable properties. Building on those results, we use available observational properties of 140 Galactic GCs to identify 29 GCs that could potentially be harbouring up to a few hundreds of BHs. Utilizing observational properties and theoretical scaling relations, we estimate the density, size and mass of the BHS in these GCs. We also calculate the total number of BHs and the fraction of BHs contained in a binary system for our shortlisted Galactic GCs. Additionally, we mention other Galactic GCs that could also contain significant number of single BHs or BHs in binary systems.

The first neutron star-neutron star (NS-NS) merger was discovered on August 17, 2017 through gravitational waves (GW170817) and followed with electromagnetic observations (Abbott et al. 2017). This merger was detected in an old elliptical galaxy with no recent star formation (Blanchard et al. 2017;Troja et al. 2017). We perform a suite of numerical calculations to understand the formation mechanism of this merger. We probe three leading formation mechanisms of double compact objects: classical isolated binary star evolution, dynamical evolution in globular clusters and nuclear cluster formation to test whether they are likely to produce NS-NS mergers in old host galaxies. Our simulations with optimistic assumptions show current NS-NS merger rates at the level of 10 −2 yr −1 from binary stars, 5 × 10 −5 yr −1 from globular clusters and 10 −5 yr −1 from nuclear clusters for all local elliptical galaxies (within 100 Mpc 3 ). These models are thus in tension with the detection of GW170817 with an observed rate 1.5 +3.2 −1.2 yr −1 (per 100 Mpc 3 ; LIGO/Virgo 90% credible limits). Our results imply that either (i) the detection of GW170817 by LIGO/Virgo at their current sensitivity in an elliptical galaxy is a statistical coincidence; or that (ii) physics in at least one of our three models is incomplete in the context of the evolution of stars that can form NS-NS mergers; or that (iii) another very efficient (unknown) formation channel with a long delay time between star formation and merger is at play.

We propose a space-based interferometer surveying the gravitational wave (GW) sky in the milli-Hz to μ-Hz frequency range. By the 2040s, the μ-Hz frequency band, bracketed in between the Laser Interferometer Space Antenna (LISA) and pulsar timing arrays, will constitute the largest gap in the coverage of the astrophysically relevant GW spectrum. Yet many outstanding questions related to astrophysics and cosmology are best answered by GW observations in this band. We show that a μ-Hz GW detector will be a truly overarching observatory for the scientific community at large, greatly extending the potential of LISA. Conceived to detect massive black hole binaries from their early inspiral with high signal-to-noise ratio, and low-frequency stellar binaries in the Galaxy, this instrument will be a cornerstone for multimessenger astronomy from the solar neighbourhood to the high-redshift Universe.

The central region of the galaxy Henize 2-10 hosts a black hole (BH) candidate with a mass Log (M BH /M ⊙ ) = 6.3 ± 1.1. While this putative black hole does not appear to coincide with any central stellar overdensity, it is surrounded by 11 young massive clusters with masses above 10 5 M ⊙ . The availability of high quality data on the structure of the galaxy and the age and mass of the clusters provides excellent initial conditions for studying the dynamical evolution of Henize 2-10's nucleus.Here we present a set of N -body simulations in which we model the future evolution of the central clusters and the black hole to understand whether and how they will merge to form a nuclear star cluster. Nuclear star clusters (NSCs) are present in a majority of galaxies with stellar mass similar to Henize 2-10. While the results depend on the choice of initial conditions, we find that a NSC with mass M NSC ≃ 4 − 6 × 10 6 M ⊙ and effective radius r NSC ≃ 2.6 − 4.1 pc will form within 0.2 Gyr. This work is the first showing, in a realistic realization of the host galaxy and its star cluster system, that the formation of a bright nucleus is a process that can happen after the formation of a central massive BH leading to a composite NSC+BH central system. The cluster merging process does not significantly affect the kinematics of the BH; when a stationary state is reached its position changes by 1 pc and its velocity by < 2 km s −1 .