The upper bound of the speed of sound in dense nuclear matter is one of the most interesting but still unsolved problems in nuclear physics. Theoretical studies in connection with recent observational data of isolated neutron stars as well as binary neutron stars systems offer an excellent opportunity to shed light on this problem. In the present work, we suggest a method to directly relate the measured tidal deformability (polarizability) of binary neutron stars system (before merger) to the maximum neutron star mass scenario and possible upper bound on the speed of sound. This method is based on the simple but efficient idea that while the upper limit of the effective tidal deformability favors soft equations of state, the recent high measured values of neutron star mass favor stiff ones. In the present work, first, using a simple well established model we parametrize the stiffness of the equation of state with the help of the speed of sound. Second, in comparison with the recent observations by LIGO/VIRGO collaboration of two events, GW170817 and GW190425, we suggest possible robust constraints. Moreover, we evaluate and postulate, in the framework of the present method, what kind of future measurements could help us to improve the stringent of the constraints on the neutron star equation of state.

On 14 August 2019, the LIGO/Virgo collaboration observed a compact object with mass $\sim {2.59}_{-0.09}^{+0.08}{M}_{\odot }$, as a component of a system where the main companion was a black hole with mass $\sim 23M_{\odot }$. A scientific debate initiated concerning the identification of the low mass component, as it falls into the neutron star–black hole mass gap. The understanding of the nature of GW190814 event will offer rich information concerning open issues, the speed of sound and the possible phase transition into other degrees of freedom. In the present work, we made an effort to probe the nuclear equation of state along with the GW190814 event. Firstly, we examine possible constraints on the nuclear equation of state inferred from the consideration that the low mass companion is a slow or rapidly rotating neutron star. In this case, the role of the upper bounds on the speed of sound is revealed, in connection with the dense nuclear matter properties. Secondly, we systematically study the tidal deformability of a possible high mass candidate existing as an individual star or as a component one in a binary neutron star system. As the tidal deformability and radius are quantities very sensitive on the neutron star equation of state, they are excellent counters on dense matter properties. We conjecture that similar isolated neutron stars or systems may exist in the universe and their possible future observation will shed light on the maximum neutron star mass problem.

In agreement with the constantly increasing gravitational wave events, new aspects of the internal structure of compact stars can be considered. A scenario in which a first-order transition takes place inside these stars is of particular interest, as it can lead, under certain conditions, to a third gravitationally stable branch (besides white dwarfs and neutron stars), the twin stars. The new branch yields stars with the same mass as normal compact stars but quite different radii. We focus on hybrid stars undergoing a hadron-to-quark phase transition near their core and how this new stable configuration arises. Emphasis is given on the aspects of the phase transition and its parametrization in two different ways—namely, with the Maxwell and Gibbs constructions. We systematically study the gravitational mass, the radius, and the tidal deformability, and we compare them with the predictions of the recent observation by the LIGO/VIRGO Collaboration, the GW170817 event, and the mass and radius limits, suggesting possible robust constraints. Moreover, we extend the study to include rotation effects on the twin star configurations. The recent discovery of the fast rotating supermassive pulsar PSR J0952-0607 triggered the efforts to constrain the equation of state and, moreover, to examine possible predictions related to the phase transition in dense nuclear matter. We pay special attention to relate the PSR J0952-0607 pulsar properties to the twin star predictions, and mainly to explore the possibility that the existence of such a massive object would rule out the existence of twin stars. Finally, we discuss the constraints on the radius and mass of the recently observed compact object within the supernova remnant HESS J1731-347. The estimations imply that this object is either the lightest known neutron star or a star with a more exotic equation of state.

Over the last few years, the detection of gravitational waves from binary neutron star systems has rekindled our hopes for a deeper understanding of the unknown nature of ultradense matter. In particular, gravitational wave constraints on the tidal deformability of a neutron star can be translated into constraints on several neutron star properties using a set of universal relations. Apart from binary neutron star mergers, supernova explosions are also important candidates for the detection of multimessenger signals. Such observations may allow us to impose significant constraints on the binding energy of neutron stars. The purpose of the present study is twofold. Firstly, we investigate the agreement of finite temperature equations of state with established universal relations. Secondly, we examine the possible existence of a universal relation between the binding energy and the dimensionless tidal deformability, which are the bulk properties connected to the most promising sources for multimessenger signals. We find that hot equations of state are not always compatible with accepted universal relations. Therefore, the use of such expressions for probing general relativity or imposing constraints on the structure of neutron stars would be inconclusive (when thermal effects are present). Additionally, we show that the binding energy and the dimensionless tidal deformability exhibit a universal trend at least for moderate neutron star masses. The latter allows us to set bounds on the binding energy of a 1.4 $M_{\odot }$ neutron star using data from the GW170817 event. Finally, we provide a relation between the compactness, the binding energy and the dimensionless tidal deformability of a neutron star that is accurate for cold and hot isentropic equations of state.

Neutron stars are the densest known objects in the universe and an ideal laboratory for the strange physics of super-condensed matter. Theoretical studies in connection with recent observational data of isolated neutron stars, as well as binary neutron stars systems, offer an excellent opportunity to provide robust solutions on the dense nuclear problem. In the present work, we review recent studies concerning the applications of various theoretical nuclear models on a few recent observations of binary neutron stars or neutron-star–black-hole systems. In particular, using a simple and well-established model, we parametrize the stiffness of the equation of state with the help of the speed of sound. Moreover, in comparison to the recent observations of two events by LIGO/VIRGO collaboration, GW170817 and GW190425, we suggest possible robust constraints. We also concentrate our theoretical study on the resent observation of a compact object with mass ∼$2.{59}_{-0.09}^{+0.08}{M}_{\odot }$ (GW190814 event), as a component of a system where the main companion was a black hole with mass ∼$23M_{\odot }$. There is scientific debate concerning the identification of the low mass component, as it falls into the neutron-star–black-hole mass gap. This is an important issue since understanding the nature of GW190814 event will offer rich information concerning the upper limit of the speed of sound in dense matter and the possible phase transition into other degrees of freedom. We systematically study the tidal deformability of a possible high-mass candidate existing as an individual star or as a component in a binary neutron star system. Finally, we provide some applications of equations of state of hot, dense nuclear matter in hot neutron stars (nonrotating and rapidly rotating with the Kepler frequency neutron stars), protoneutron stars, and binary neutron star merger remnants.

We investigate the hypothetical X17 boson on neutron stars and quark stars (QSs) using various hadronic equation of states (EoSs) with phenomenological or microscopic origin. Our aim is to set realistic constraints on its coupling constant and the mass scaling, with respect to causality and various possible upper mass limits and the dimensionless tidal deformability ${\mathrm{\Lambda }}_{1.4}$. In particular, we pay special attention to two main phenomenological parameters of the X17, one is related to the coupling constant $\mathrm{g}$ that it has with hadrons or quarks and the other with the in-medium effects through regulator $\mathrm{C}$. Both are very crucial concerning the contribution on the total energy density and pressure. In the case of considering the X17 as a carrier of nuclear force in relativistic mean field theory, an admixture into the vector boson segment was constrained by 20% and 30%. In our investigation, we came to the general conclusion that the effect of the hypothetical X17 both on neutron and QSs is constrained mainly by the causality limit, which is a specific property of each EoS, and it depends on the interplay between the two main parameters, the interaction coupling $\mathrm{g}$ and the in-medium effects regulator $\mathrm{C}$. These effects are more pronounced in the case of QSs concerning all the bulk properties.