Neutron star collapse and gravitational waves with a non-convex equation of state

© 2019 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society. The thermodynamical properties of the equation of state (EoS) of high-density matter (above nuclear saturation density) and the possible existence of exotic states such as phase transitions from nuclear/hadronic matter into quark-gluon plasma, or the appearance of hyperons, may critically influence the stability and dynamics of compact relativistic stars. From a theoretical point of view, establishing the existence of those states requires the analysis of the 'convexity' of the EoS. We show indications of the existence of regions in the dense-matter EoS where the thermodynamics may be non-convex as a result of a non-monotonic dependence of the sound speed with the rest-mass density. When this happens, non-conventional dynamics may develop. In this paper we investigate the effects of a phenomenological, non-convex EoS on the equilibrium structure of stable compact stars and on the dynamics of unstable neutron stars that collapse gravitationally to black holes, both for spherically symmetric and uniformly rotating configurations. We show how the dynamics of the collapse with a non-convex EoS departs from the convex case, leaving distinctive imprints on the gravitational waveforms. The astrophysical significance of these results for microphysical EoSs is discussed.