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 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.

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.