The space-based Laser Interferometer Space Antenna (LISA) will be able to observe the gravitational-wave signals from systems comprised of a massive black hole and a stellar-mass compact object. These systems are known as extreme-mass-ratio inspirals (EMRIs) and are expected to complete ∼ 10 4 -10 5 cycles in band, thus allowing exquisite measurements of their parameters. In this work, we attempt to quantify the astrophysical uncertainties affecting the predictions for the number of EMRIs detectable by LISA, and find that competing astrophysical assumptions produce a variance of about three orders of magnitude in the expected intrinsic EMRI rate. However, we find that irrespective of the astrophysical model, at least a few EMRIs per year should be detectable by the LISA mission, with up to a few thousands per year under the most optimistic astrophysical assumptions. We also investigate the precision with which LISA will be able to extract the parameters of these sources. We find that typical fractional statistical errors with which the intrinsic parameters (redshifted masses, massive black hole spin and orbital eccentricity) can be recovered are ∼ 10 −6 -10 −4 . Luminosity distance (which is required to infer true masses) is inferred to about 10% precision and sky position is localized to a few square degrees, while tests of the multipolar structure of the Kerr metric can be performed to percent-level precision or better.

Massive black hole binary systems, with masses in the range ∼104–1010 M⊙, are among the primary sources of gravitational waves in the frequency window ∼10−9–0.1 Hz. Pulsar Timing Arrays (PTAs) and the Laser Interferometer Space Antenna (LISA) are the observational means by which we will be able to observe gravitational radiation from these systems. We carry out a systematic study of the generation of the stochastic gravitational‐wave background from the cosmic population of massive black hole binaries. We consider a wide variety of assembly scenarios and we estimate the range of signal strength in the frequency band accessible to PTAs. We show that regardless of the specific model of massive black hole binaries formation and evolution, the characteristic amplitude hc of the gravitational‐wave stochastic background at 10−8 Hz varies by less than a factor of 2. However, taking into account the uncertainties surrounding the actual key model parameters, the amplitude lies in the interval hc(f= 10−8 Hz) ≈ 5 × 10−16–8 × 10−15. The most optimistic predictions place the signal level at a factor of ≈3 below the current sensitivity of PTAs, but within the detection range of the complete Parkes PTA for a wide variety of models, and of the future Square‐Kilometer Array PTA for all the models considered here. We also show that at frequencies ≳10−8 Hz, the frequency dependency of the generated background follows a power law significantly steeper than hc∝f−2/3, which has been considered so far; the value of the spectral index depends on the actual assembly scenario and provides therefore an additional opportunity to extract astrophysical information about the cosmic population of massive black holes. Finally, we show that LISA observations of individual resolvable massive black hole binaries are complementary and orthogonal to PTA observations of a stochastic background from the whole population in the Universe. In fact, the detection of gravitational radiation in both frequency windows will enable us to fully characterize the cosmic history of massive black holes.

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 review the expected science performance of the New Gravitational-Wave Observatory (NGO, a.k.a. eLISA), a mission under study by the European Space Agency for launch in the early 2020s. eLISA will survey the low-frequency gravitational-wave sky (from 0.1 mHz to 1 Hz), detecting and characterizing a broad variety of systems and events throughout the Universe, including the coalescences of massive black holes brought together by galaxy mergers; the inspirals of stellar-mass black holes and compact stars into central galactic black holes; several millions of ultra-compact binaries, both detached and mass transferring, in the Galaxy; and possibly unforeseen sources such as the relic gravitational-wave radiation from the early Universe. eLISA's high signal-tonoise measurements will provide new insight into the structure and history of the Universe, and they will test general relativity in its strong-field dynamical regime.