One century after its formulation, Einsteinʼs general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when Class. Quantum Grav. 32 (2015) 243001Topical Review physical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einsteinʼs theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

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’.

All ten LIGO/Virgo binary black hole (BH-BH) coalescences reported following the O1/O2 runs have near-zero effective spins. There are only three potential explanations for this. If the BH spin magnitudes are large, then: (i) either both BH spin vectors must be nearly in the orbital plane or (ii) the spin angular momenta of the BHs must be oppositely directed and similar in magnitude. Then there is also the possibility that (iii) the BH spin magnitudes are small. We consider the third hypothesis within the framework of the classical isolated binary evolution scenario of the BH-BH merger formation. We test three models of angular momentum transport in massive stars: a mildly efficient transport by meridional currents (as employed in the Geneva code), an efficient transport by the Tayler-Spruit magnetic dynamo (as implemented in the MESA code), and a very-efficient transport (as proposed by Fuller et al.) to calculate natal BH spins. We allow for binary evolution to increase the BH spins through accretion and account for the potential spin-up of stars through tidal interactions. Additionally, we update the calculations of the stellar-origin BH masses, including revisions to the history of star formation and to the chemical evolution across cosmic time. We find that we can simultaneously match the observed BH-BH merger rate density and BH masses and BH-BH effective spins. Models with efficient angular momentum transport are favored. The updated stellar-mass weighted gas-phase metallicity evolution now used in our models appears to be key for obtaining an improved reproduction of the LIGO/Virgo merger rate estimate. Mass losses during the pair-instability pulsation supernova phase are likely to be overestimated if the merger GW170729 hosts a BH more massive than 50 M⊙. We also estimate rates of black hole-neutron star (BH-NS) mergers from recent LIGO/Virgo observations. If, in fact. angular momentum transport in massive stars is efficient, then any (electromagnetic or gravitational wave) observation of a rapidly spinning BH would indicate either a very effective tidal spin up of the progenitor star (homogeneous evolution, high-mass X-ray binary formation through case A mass transfer, or a spin- up of a Wolf-Rayet star in a close binary by a close companion), significant mass accretion by the hole, or a BH formation through the merger of two or more BHs (in a dense stellar cluster).

The dynamics of precessing binary black holes (BBHs) in the post-Newtonian regime has a strong timescale hierarchy: the orbital timescale is very short compared to the spin-precession timescale which, in turn, is much shorter than the radiation-reaction timescale on which the orbit is shrinking due to gravitational-wave emission. We exploit this timescale hierarchy to develop a multiscale analysis of BBH dynamics elaborating on the analysis of Kesden et al. [Phys. Rev. Lett. 114, 081103 (2015)]. We solve the spin-precession equations analytically on the precession time and then implement a quasiadiabatic approach to evolve these solutions on the longer radiation-reaction time. This procedure leads to an innovative "precession-averaged" post-Newtonian approach to studying precessing BBHs. We use our new solutions to classify BBH spin precession into three distinct morphologies, then investigate phase transitions between these morphologies as BBHs inspiral. These precession-averaged post-Newtonian inspirals can be efficiently calculated from arbitrarily large separations, thus making progress towards bridging the gap between astrophysics and numerical relativity.

Only numerical relativity simulations can capture the full complexities of binary black hole mergers. These simulations, however, are prohibitively expensive for direct data analysis applications such as parameter estimation. We present two new fast and accurate surrogate models for the outputs of these simulations: the first model, NRSur7dq4, predicts the gravitational waveform and the second model, NRSur7dq4Remnant, predicts the properties of the remnant black hole. These models extend previous 7-dimensional, non-eccentric precessing models to higher mass ratios, and have been trained against 1528 simulations with mass ratios q ≤ 4 and spin magnitudes χ1, χ2 ≤ 0.8, with generic spin directions. The waveform model, NRSur7dq4, which begins about 20 orbits before merger, includes all ≤ 4 spin-weighted spherical harmonic modes, as well as the precession frame dynamics and spin evolution of the black holes. The final black hole model, NRSur7dq4Remnant, models the mass, spin, and recoil kick velocity of the remnant black hole. In their training parameter range, both models are shown to be more accurate than existing models by at least an order of magnitude, with errors comparable to the estimated errors in the numerical relativity simulations. We also show that the surrogate models work well even when extrapolated outside their training parameter space range, up to mass ratios q = 6.

Advanced LIGO detectors at Hanford and Livingston made two confirmed and one marginal detection of binary black holes during their first observing run. The first event, GW150914, was from the merger of two black holes much heavier that those whose masses have been estimated so far, indicating a formation scenario that might differ from "ordinary" stellar evolution. One possibility is that these heavy black holes resulted from a previous merger. When the progenitors of a black hole binary merger result from previous mergers, they should (on average) merge later, be more massive, and have spin magnitudes clustered around a dimensionless spin ∼ 0.7. Here we ask the following question: can gravitational-wave observations determine whether merging black holes were born from the collapse of massive stars ("first generation"), rather than being the end product of earlier mergers ("second generation")? We construct simple, observationally motivated populations of black hole binaries, and we use Bayesian model selection to show that measurements of the masses, luminosity distance (or redshift), and "effective spin" of black hole binaries can indeed distinguish between these different formation scenarios.

We study the expected spin misalignments of merging binary black holes formed in isolation by combining state-of-the-art population-synthesis models with efficient post-Newtonian evolutions, thus tracking sources from stellar formation to gravitational-wave detection. We present extensive predictions of the properties of sources detectable by both current and future interferometers. We account for the fact that detectors are more sensitive to spinning black-hole binaries with suitable spin orientations and find that this significantly impacts the population of sources detectable by LIGO, while this is not the case for third-generation detectors. We find that three formation pathways, differentiated by the order of core collapse and common-envelope phases, dominate the observed population, and that their relative importance critically depends on the recoils imparted to black holes at birth. Our models suggest that measurements of the "effective-spin" parameter χ eff will allow for powerful constraints. For instance, we find that the role of spin magnitudes and spin directions in χ eff can be largely disentangled, and that the symmetry of the effective-spin distribution is a robust indicator of the binary's formation history. Our predictions for individual spin directions and their precessional morphologies confirm and extend early toy models, while exploring substantially more realistic and broader sets of initial conditions. Our main conclusion is that specific subpopulations of black-hole binaries will exhibit distinctive precessional dynamics: these classes include (but are not limited to) sources where stellar tidal interactions act on sufficiently short timescales, and massive binaries produced in pulsational pair-instability supernovae. Measurements of black-hole spin orientations have enormous potential to constrain specific evolutionary processes in the lives of massive binary stars.

We derive an effective potential for binary black hole (BBH) spin precession at second post-Newtonian order. This effective potential allows us to solve the orbit-averaged spin-precession equations analytically for arbitrary mass ratios and spins. These solutions are quasiperiodic functions of time: after a fixed period, the BBH spins return to their initial relative orientations and jointly precess about the total angular momentum by a fixed angle. Using these solutions, we classify BBH spin precession into three distinct morphologies between which BBHs can transition during their inspiral. We also derive a precessionaveraged evolution equation for the total angular momentum that can be integrated on the radiation-reaction time and identify a new class of spin-orbit resonances that can tilt the direction of the total angular momentum during the inspiral. Our new results will help efforts to model and interpret gravitational waves from generic BBH mergers and predict the distributions of final spins and gravitational recoils. Introduction.-The classic two-body problem was a major engine of historical progress in physics and astronomy. This problem can be solved analytically in Newtonian gravity; its solutions are the well-known Keplerian orbits. The analogs to Newtonian point masses in general relativity are binary black holes (BBHs). Astrophysical BBHs have spins S i [1] in addition to their masses m i [the masses determine the total mass M ≡ m 1 þ m 2 , mass ratio q ≡ m 2 =m 1 ≤ 1 and symmetric mass ratio η ≡ m 1 m 2 =M 2 ¼ q=ð1 þ qÞ 2 ]. Full solutions to the two-body problem in general relativity must, therefore, include spin evolution in addition to orbital motion. Einstein's equations must be solved numerically [2][3][4] when the binary separation r is comparable to the gravitational radius r g ≡ GM=c 2 , but post-Newtonian (PN) approximations may be used when r ≫ r g . BBH evolution in the PN limit occurs on three distinct time scales: the orbital time t orb ∼ ðr 3 =GMÞ 1=2 on which the binary separation r evolves, the precession time t pre ∼ c 2 r 5=2 = ½ηðGMÞ 3=2 ∼ ðt orb =ηÞðr=r g Þ on which the spin directions change, and the radiation-reaction time t RR ∼ E= jdE GW =dtj ∼ c 5 r 4 =½ηðGMÞ 3 ∼ ðt orb =ηÞðr=r g Þ 5=2 on which the energy E ¼ −GηM 2 =ð2rÞ and orbital angular momentum L ¼ ηðrGM 3 Þ 1=2 decrease.The hierarchy t orb ≪ t pre ≪ t RR implies that when considering evolution on one time scale, quantities evolving on a shorter (longer) time scale can be averaged (held constant). This has been used to derive orbit-averaged spin-precession equations _ S i ¼Ω i × S i [5][6][7][8], where the precession frequenciesΩ i depend on the orbital angular momentum L and spins S i but not on the instantaneous