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.

A Reissner-Nordström black hole (BH) is superradiantly unstable against spherical perturbations of a charged scalar field enclosed in a cavity, with a frequency lower than a critical value. We use numerical relativity techniques to follow the development of this unstable system-dubbed a charged BH bombinto the nonlinear regime, solving the full Einstein-Maxwell-Klein-Gordon equations, in spherical symmetry. We show that (i) the process stops before all the charge is extracted from the BH, and (ii) the system settles down into a hairy BH: a charged horizon in equilibrium with a scalar field condensate, whose phase is oscillating at the (final) critical frequency. For a low scalar field charge q, the final state is approached smoothly and monotonically. For large q, however, the energy extraction overshoots, and an explosive phenomenon, akin to a bosenova, pushes some energy back into the BH. The charge extraction, by contrast, does not reverse.

We study the evolution of a massive scalar field surrounding a Schwarzschild black hole and find configurations that can survive for arbitrarily long times, provided the black hole or the scalar field mass is small enough. In particular, both ultralight scalar field dark matter around supermassive black holes and axionlike scalar fields around primordial black holes can survive for cosmological times. Moreover, these results are quite generic in the sense that fairly arbitrary initial data evolve, at late times, as a combination of those long-lived configurations.

Frequency domain studies have recently demonstrated that charged scalar fields exhibit fast growing superradiant instabilities when interacting with charged black holes in a cavity. Here, we present a time domain analysis of the long time evolution of test charged scalar field configurations on the Reissner-Nordström background, with or without a mirror-like boundary condition. Initial data is taken to be either a Gaussian wave packet or a regularised (near the horizon) quasi-bound state. Then, Fourier transforming the data obtained in the evolution confirms the results obtained in the frequency domain analysis, in particular for the fast growing modes. We show that spherically symmetric (ℓ = 0) modes have even faster growth rates than the ℓ = 1 modes for 'small' field charge. Thus, our study confirms that this setup is particularly promising for considering the non-linear development of the superradiant instability, since the fast growth makes the signal overcome the numerical error that dominates for small growth rates, and the analysis may be completely done in spherical symmetry.

Confined scalar fields, either by a mass term or by a mirror-like boundary condition, have unstable modes in the background of a Kerr black hole. Assuming a time dependence as e −iωt , the growth time-scale of these unstable modes is set by the inverse of the (positive) imaginary part of the frequency, Im(ω), which reaches a maximum value of the order of Im(ω)M ∼ 10 −5 , attained for a mirror-like boundary condition, where M is the black hole mass. In this paper we study the minimally coupled Klein-Gordon equation for a charged scalar field in the background of a Reissner-Nordström black hole and show that the unstable modes, due to a mirror-like boundary condition, can grow several orders of magnitude faster than in the rotating case: we have obtained modes with up to Im(ω)M ∼ 0.07. We provide an understanding, based on an analytic approximation, to why the instability in the charged case has a smaller timescale than in the rotating case. This faster growth, together with the spherical symmetry, makes the charged case a promising model for studies of the fully non-linear development of superradiant instabilities.

Classical scalar fields have been proposed as possible candidates for the dark matter component of the universe. Given the fact that super-massive black holes seem to exist at the center of most galaxies, in order to be a viable candidate for the dark matter halo a scalar field configuration should be stable in the presence of a central black hole, or at least be able to survive for cosmological time-scales. In the present work we consider a scalar field as a test field on a Schwarzschild background, and study under which conditions one can obtain long-lived configurations. We present a detailed study of the Klein-Gordon equation in the Schwarzschild spacetime, both from an analytical and numerical point of view, and show that indeed there exist quasi-stationary solutions that can remain surrounding a black hole for large time-scales.Comment: 34 pages, 13 figure

We present new, fully nonlinear numerical solutions to the static, spherically symmetric Einstein-Klein-Gordon system for a collection of an arbitrary odd number N of complex scalar fields with an internal U (N) symmetry and no self-interactions. These solutions, which we dub ℓ-boson stars, are parametrized by an angular momentum number ℓ = (N − 1)/2, an excitation number n, and a continuous parameter representing the amplitude of the fields. They are regular at every point and possess a finite total mass. For ℓ = 0 the standard spherically symmetric boson stars are recovered. We determine their generalizations for ℓ > 0, and show that they give rise to a large class of new static configurations which might have a much larger compactness ratio than ℓ = 0 stars.

Vector boson stars, or Proca stars, have been recently obtained as fully nonlinear numerical solutions of the Einstein-(complex)-Proca system [1]. These are self-gravitating, everywhere nonsingular, horizonless Bose-Einstein condensates of a massive vector field, which resemble in many ways, but not all, their scalar cousins, the well-known (scalar) boson stars. In this paper we report fully nonlinear numerical evolutions of Proca stars, focusing on the spherically symmetric case, with the goal of assessing their stability and the end point of the evolution of the unstable stars. Previous results from linear perturbation theory indicate that the separation between stable and unstable configurations occurs at the solution with maximal ADM mass. Our simulations confirm this result. Evolving numerically unstable solutions, we find, depending on the sign of the binding energy of the solution and on the perturbation, three different outcomes: (i) migration to the stable branch, (ii) total dispersion of the scalar field, or (iii) collapse to a Schwarzschild black hole. In the latter case, a long-lived Proca field remnant-a Proca wig-composed by quasibound states, may be seen outside the horizon after its formation, with a lifetime that scales inversely with the Proca mass. We comment on the similarities/differences with the scalar case as well as with neutron stars.