• collapse
• merging
• stable configurations

The recent multi-signals detection from the merging of two neutron stars has definitely sanctioned a new era with which probe the nature of these objects. Neutron stars indeed are some of the densest structures known in astrophysics with typical dimensions approaching the relative Schwarzschild radius. In particular compact objects resulting from the merger of binary neutron stars (BNS) are composed by matter whose density could exceed that of nuclear saturation. Therefore these kind of stars represents an ideal laboratory where provide connection between nuclear physics and astrophysics.
In this work we mainly focus on the effects of differential rotation, on the properties and evolution of the compact objects formed in BNS merger. In line with previous works we find that the more evident effect of differential rotation is to increase the maximum possible compact star mass with respect to the case of non rotating and rigidly rotating stars. The total mass (M1 + M2) of the two merging NSs is the crucial parameter which control the final fate of the compact object formed in the BNS merger. In other words depending on the values of (M1 + M2) one could have (i) a prompt collapse to a BH, (ii) a delayed formation of a BH, or (iii) the formation of a stable NS. The fate followed by the structures will produce different GW signals in the post-merger phase. Thus differentially rotating post-merger compact objects with ”large mass” (larger than the maximum mass for rigidly rotating neutron stars, i.e. the so called hypermassive configurations) can be temporarily stabilized and then form a BH within the relaxation time of differential rotation to rigid-body rotation. The study of differentially rotating relativistic stars is thus of great importance for the interpretation and modeling of the gravitational wave signal from BNS mergers.
At the moment several works have been developed using schematic EoSs and particularly polytropic EoSs. On the contrary we use ”realistic EoSs” of nuclear matter (namely EoSs derived using various approaches to describe strong-interacting quantum many-body systems) at T = 0 namely neglecting thermal effects.
Then in the present work we study differentially rotating compact stars in general relativity using two open source codes, the Lorene and the RNS codes, which have been widely used by various research groups working in numerical relativity. No hydrodynamical simulations have been performed so that our analysis are based on ”snapshots” of sequences of models.
All the evolutionary pattern considered are based on the conservation of the angular momentum meaning that no dissipation processes have been taken into consideration.
Moreover our results from structures rotating differentially show models whose maximum mass in the mass-shed sequence arrives to be ∼ 40.6% greater than the uniform rotating counterpart and about ∼ 52.6% greater than the static one for the most extreme case considered, in the space of the differential parameters.Therefore interesting findings obtained concern the mass range of the models from which it is possible determine the fate of a remnant of BNS and so what kind of features characterizes a stable star or the general GW signal we should expect. In effect since the product of coalescence of NSs may be temporarily stabilized by differential rotation, then delayed GW could be emitted in a step-driven collapsing process.
Finally considering the findings of the present work, we have devoted the final section to perform an analysis of our models based on the informations coming from the GW170817 event.