Gravitational waves from neutron star mergers and their relation to the nuclear equation of state

In this article, I introduce ideas and techniques to extract information about the equation of state of matter at very high densities from gravitational waves emitted before, during and after the merger of binary neutron stars. I also review current work and results on the actual use of the first gravitational-wave observation of a neutron-star merger to set constraints on properties of such equation of state. In passing, I also touch on the possibility that what we observe in gravitational waves are not neutron stars, but something more exotic. In order to make this article more accessible, I also review the dynamics and gravitational-wave emission of neutron-star mergers in general, with focus on numerical simulations and on which representations of the equation of state are used for studies on binary systems. (C) 2019 Elsevier B.V. All rights reserved.