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.

Numerical-relativity simulations for the merger of binary neutron stars are performed for a variety of equations of state (EOSs) and for a plausible range of the neutron-star mass, focusing primarily on the properties of the material ejected from the system. We find that a fraction of the material is ejected as a mildly relativistic and mildly anisotropic outflow with the typical and maximum velocities ∼ 0.15 -0.25c and ∼ 0.5 -0.8c (where c is the speed of light), respectively, and that the total ejected rest mass is in a wide range 10 −4 -10 −2 M , which depends strongly on the EOS, the total mass, and the mass ratio. The total kinetic energy ejected is also in a wide range between 10 49 and 10 51 ergs. The numerical results suggest that for a binary of canonical total mass 2.7M , the outflow could generate an electromagnetic signal observable by the planned telescopes through the production of heavy-element unstable nuclei via the r-process [1][2][3] or through the formation of blast waves during the interaction with the interstellar matter [4], if the EOS and mass of the binary are favorable ones.

We perform a numerical-relativity simulation for the merger of binary neutron stars with 6 nucleartheory-based equations of state (EOSs) described by piecewise polytropes. Our purpose is to explore the dependence of the dynamical behavior of the binary neutron star merger and resulting gravitational waveforms on the EOS of the supernuclear-density matter. The numerical results show that the merger process and the first outcome are classified into three types; (i) a black hole is promptly formed, (ii) a short-lived hypermassive neutron star (HMNS) is formed, (iii) a long-lived HMNS is formed. The type of the merger depends strongly on the EOS and on the total mass of the binaries. For the EOS with which the maximum mass is larger than 2M⊙, the lifetime of the HMNS is longer than 10 ms for a total mass m0 = 2.7M⊙. A recent radio observation suggests that the maximum mass of spherical neutron stars is Mmax ≥ 1.97 ± 0.04M⊙ in one σ level. This fact and our results support the possible existence of a HMNS soon after the onset of the merger for a typical binary neutron star with m0 = 2.7M⊙. We also show that the torus mass surrounding the remnant black hole is correlated with the type of the merger process; the torus mass could be large, ≥ 0.1M⊙, in the case that a long-lived HMNS is formed. We also show that gravitational waves carry information of the merger process, the remnant, and the torus mass surrounding a black hole.

Ultracompact objects are self-gravitating systems with a light ring. It was recently suggested that fluctuations in the background of these objects are extremely long-lived and might turn unstable at the nonlinear level, if the object is not endowed with a horizon. If correct, this result has important consequences: objects with a light ring are black holes. In other words, the nonlinear instability of ultracompact stars would provide a strong argument in favor of the "black hole hypothesis," once electromagnetic or gravitational-wave observations confirm the existence of light rings. Here we explore in some depth the mode structure of ultracompact stars, in particular constant-density stars and gravastars. We show that the existence of very long-lived modes -localized near a second, stable null geodesic -is a generic feature of gravitational perturbations of such configurations. Already at the linear level, such modes become unstable if the object rotates sufficiently fast to develop an ergoregion. Finally, we conjecture that the long-lived modes become unstable under fragmentation via a Dyson-Chandrasekhar-Fermi mechanism at the nonlinear level. Depending on the structure of the star, it is also possible that nonlinearities lead to the formation of small black holes close to the stable light ring. Our results suggest that the mere observation of a light ring is a strong evidence for the existence of black holes.

We investigate properties of material ejected dynamically in the merger of black hole-neutron star binaries by numerical-relativity simulations. We systematically study the dependence of ejecta properties on the mass ratio of the binary, spin of the black hole, and equation of state of the neutron-star matter. Dynamical mass ejection is driven primarily by tidal torque, and the ejecta is much more anisotropic than that from binary neutron star mergers. In particular, the dynamical ejecta is concentrated around the orbital plane with a half opening angle of 10• -20• and often sweeps out only a half of the plane. The ejecta mass can be as large as ∼ 0.1M⊙, and the velocity is subrelativistic with ∼ 0.2-0.3c for typical cases. The ratio of the ejecta mass to the bound mass (disk and fallback components) is larger, and the ejecta velocity is larger, for larger values of the binary mass ratio, i.e., for larger values of the black hole mass. The remnant black hole-disk system receives a kick velocity of O(100) km s −1 due to the ejecta linear momentum, and this easily dominates the kick velocity due to gravitational radiation. Structures of postmerger material, velocity distribution of the dynamical ejecta, fallback rates, and gravitational waves are also investigated. We also discuss the effect of ejecta anisotropy on electromagnetic counterparts, specifically a macronova/kilonova and synchrotron radio emission, developing analytic models.