When surrounded by a transparent emission region, black holes are expected to reveal a dark shadow caused by gravitational light bending and photon capture at the event horizon. To image and study this phenomenon, we have assembled the Event Horizon Telescope, a global very long baseline interferometry array observing at a wavelength of 1.3 mm. This allows us to reconstruct event-horizon-scale images of the supermassive black hole candidate in the center of the giant elliptical galaxy M87. We have resolved the central compact radio source as an asymmetric bright emission ring with a diameter of 42±3 μas, which is circular and encompasses a central depression in brightness with a flux ratio 10:1. The emission ring is recovered using different calibration and imaging schemes, with its diameter and width remaining stable over four different observations carried out in different days. Overall, the observed image is consistent with expectations for the shadow of a Kerr black hole as predicted by general relativity. The asymmetry in brightness in the ring can be explained in terms of relativistic beaming of the emission from a plasma rotating close to the speed of light around a black hole. We compare our images to an extensive library of ray-traced general-relativistic magnetohydrodynamic simulations of black holes and derive a central mass of M=(6.5±0.7)×10 9 M e . Our radiowave observations thus provide powerful evidence for the presence of supermassive black holes in centers of galaxies and as the central engines of active galactic nuclei. They also present a new tool to explore gravity in its most extreme limit and on a mass scale that was so far not accessible.

Advanced gravitational wave interferometers, currently under realization, will soon permit the detection of gravitational waves from astronomical sources. To open the era of precision gravitational wave astronomy, a further substantial improvement in sensitivity is required. The future space-based Laser Interferometer Space Antenna and the third-generation ground-based observatory Einstein Telescope (ET) promise to achieve the required sensitivity improvements in frequency ranges. The vastly improved sensitivity of the third generation of gravitational wave observatories could permit detailed measurements of the sources' physical parameters and could complement, in a multi-messenger approach, the observation of signals emitted by cosmological sources obtained through other kinds of telescopes. This paper describes the progress of the ET project which is currently in its design study phase.

The book provides a lively and approachable introduction to the main concepts and techniques of relativistic hydrodynamics in a form which will appeal to physicists at advanced undergraduate and postgraduate levels. The book is divided into three parts. The first part deals with the physical aspects of relativistic hydrodynamics, touching on fundamental topics such as kinetic theory, equations of state, mathematical aspects of hyperbolic partial differential equations, linear and nonlinear waves in fluids, reaction fronts, and the treatment of non-ideal fluids. The second part provides an introductory but complete description of those numerical methods currently adopted in the solution of the relativistic-hydrodynamic equations. Starting from traditional finite-difference methods, modern high-resolution shock-capturing methods are discussed with special emphasis on Godunov upwind schemes based on Riemann solvers. High-order schemes are also treated, focusing on essentially non-oscillatory and weighted non-oscillatory methods, Galerkin methods and on modern ADER approaches. Finally, the third part of the book is devoted to applications and considers several physical and astrophysical systems for which relativistic hydrodynamics plays a crucial role. Several non-self-gravitating systems are first studied, including self-similar flows, relativistic blast waves, spherical flows onto a compact object, relativistic accreting disks, relativistic jets and heavy-ion collisions. Self-gravitating systems are also considered, from isolated stars, to more dynamical configurations such as the collapse to a black hole or the dynamics of binary systems. The book is especially recommended to astrophysicists, particle physicists and applied mathematicians.

Combining the GW observations of merging systems of binary neutron stars and quasi-universal relations, we set constraints on the maximum mass that can be attained by nonrotating stellar models of neutron stars. More specifically, exploiting the recent observation of the GW event GW 170817 and drawing from basic arguments on kilonova modeling of GRB 170817A, together with the quasi-universal relation between the maximum mass of nonrotating stellar models M TOV and the maximum mass supported through uniform rotation M max = 1.20 +0.02 −0.05 M TOV we set limits for the maximum mass to be 2.01 +0.04 −0.04 ≤ M TOV /M 2.16 +0.17 −0.15 , where the lower limit in this range comes from pulsar observations. Our estimate, which follows a very simple line of arguments and does not rely on the modeling of the electromagnetic signal in terms of numerical simulations, can be further refined as new detections become available. We briefly discuss the impact that our conclusions have on the equation of state of nuclear matter.