Binary neutron star mergers in the gravitational wave era

After the first direct observations of gravitational waves generated by the coalescence of binary black hole systems, expectations about the possibility to reveal binary neutron star systems are growing. Beyond the chance to probe the ``strong'' gravity regime and thus the validity of general relativity, these events will allow us to study extreme physical conditions not reproducible on Earth and in particular the behaviour of matter at supranuclear densities. Furthermore, the emission of gravitational waves is accompanied by a wide set of electromagnetic signals which cover the entire spectrum, from gamma to radio, paving the way to a multi-messenger astrophysics. The present work will give a brief overview of these systems, from the formation to the dynamics, with emphasis on the gravitational and electromagnetic emission and on the present and future detection perspectives. In the first chapter we will introduce neutron stars, starting with a short historical background, and we will report some general information about their structure and present observations. We will give the foundation for a theoretical model of such objects. In the second chapter we will discuss the formation channels for a binary system and the three phases of binary system coalescence. In the third chapter we will solve the linearized Einstein field equations, showing that they admit a wave solution. We will then understand how the gravitational wave emission is related to the stress-energy tensor of the source, and we will apply the theory to the case of a binary system. In the fourth chapter we will give an overview of the most promising electromagnetic counterparts to the gravitational wave signal from binary neutron star mergers.