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’.

We consider axially symmetric, rotating boson stars. Their flat-space limits represent spinning Q-balls. We discuss their properties and determine their domain of existence. Q-balls and boson stars are stationary solutions and exist only in a limited frequency range. The coupling to gravity gives rise to a spiral-like frequency dependence of the boson stars. We address the flat-space limit and the limit of strong gravitational coupling. For comparison we also determine the properties of spherically symmetric Q-balls and boson stars.

We construct traversable wormholes in dilatonic Einstein-Gauss-Bonnet theory in four spacetime dimensions, without needing any form of exotic matter. We determine their domain of existence, and show that these wormholes satisfy a generalized Smarr relation. We demonstrate linear stability with respect to radial perturbations for a subset of these wormholes.

Gravitational waves emitted by distorted black holes-such as those arising from the coalescence of two neutron stars or black holes-carry not only information about the corresponding spacetime but also about the underlying theory of gravity. Although general relativity remains the simplest, most elegant, and viable theory of gravitation, there are generic and robust arguments indicating that it is not the ultimate description of the gravitational universe. Here, we focus on a particularly appealing extension of general relativity, which corrects Einstein's theory through the addition of terms which are second order in curvature: the topological Gauss-Bonnet invariant coupled to a dilaton. We study gravitational-wave emission from black holes in this theory and (i) find strong evidence that black holes are linearly (mode) stable against both axial and polar perturbations, (ii) discuss how the quasinormal modes of black holes can be excited during collisions involving black holes, and finally (iii) show that future ringdown detections with a large signal-to-noise ratio would improve current constraints on the coupling parameter of the theory.