Phase transitions in neutron stars and their links to gravitational waves

The recent direct observation of gravitational wave event GW170817 and its GRB 170817 A signal has opened up a new window to studying neutron stars and heralds a new era of astronomy referred to as the multimessenger astronomy. Both gravitational and electromagnetic waves from a single astrophysical source have been detected for the first time. This combined detection offers an unprecedented opportunity to place constraints on the neutron star matter equation of state (EoS). The existence of a possible hadron-quark phase transition in the central regions of neutron stars is associated with the appearance of g modes, which are extremely important as they could signal the presence of a pure quark matter core in the centers of neutron stars. Observations of g modes with frequencies between 1 and 1.5 kHz could be interpreted as evidence of a sharp hadron-quark phase transition in the cores of neutron stars. In this article, we shall review the description of the dense matter composing neutron stars, the determination of the EoS of such matter, and the constraints imposed by astrophysical observations of these fascinating compact objects.