Gravitational-wave and X-ray probes of the neutron star equation of state

The physics of neutron stars is a remarkable combination of Einstein’s theory of general relativity and nuclear physics. Their interiors harbour extreme matter that cannot be probed in the laboratory. At such high densities and pressures, their cores may consist predominantly of exotic matter, such as free quarks or hyperons. Observations from the Laser Interferometer Gravitational-Wave Observatory (LIGO) and other gravitational-wave interferometers and X-ray observations from the Neutron Star Interior Composition Explorer (NICER) are beginning to provide information about neutron star cores and, therefore, about the mechanisms that make such objects possible. In this Review, we discuss what has been learned so far about the physics of neutron stars from gravitational-wave and X-ray observations. We focus on what has been observed with certainty and what should be observable in the near future, emphasizing the physical understanding that these new observations will bring.