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⊙ 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.

In the past few years, a lot of studies devoted to the discovery of universal relations (equation of state independent relations). The significance of such expressions can be understood if we consider that they offer the opportunity for testing general relativity in a way that is independent of the nuclear equation of state and they also allow us to impose constraints on the structure of neutron stars. The aim of this work is twofold. Firstly, we wish to clarify if hot equations of state are able to reproduce established universal relations. Secondly, we investigate a possible universal connection between the binding energy and the dimensionless tidal deformability of a neutron star. These two bulk properties are associated with two very important candidates for multimessenger signals, binary neutron star mergers and supernova explosions. We find that the predictions of hot equations of state do not agree with the predictions from accepted universal relations. Subsequently,  the use of universal relations, when thermal effects are present, may be erroneous. Additionally, we find that, for moderate neutron star masses, the binding energy and the dimensionless tidal deformability of a neutron star satisfy a universal relation. The latter allows us to impose constraints on the binding energy of 1.4 Msun neutron star, using information from the analysis of the GW170817 event. Finally, we are able to present a universal relation between the compactness, the binding energy and the dimensionless tidal deformability, which is independent of the employed equation of state for zero and finite temperature.

The observation and distinction of two compact stars with identical mass but different radius would be a clear sign of hadron-quark phase transition in nuclear matter. Motivated by studies searching for significant deviations in the observables of twin stars, we investigate the differences that manifest in their r-mode instability windows and spin-down evolution. Firstly, we obtain a set of hybrid equations of state (which predict the existence of a third stable branch of compact objects) by employing the well-known Maxwell construction, within the phenomenological framework of constant speed of sound parametrization. Then, we systematically study the influence of certain parameters, such as the energy density jump (in the resulting hybrid equation of state) and the crust elasticity, on the deviations between the r-mode instability windows and spin-down evolution of twin stars. We conclude that two stars with identical mass and fairly similar spin frequency and temperature, may behave differently with respect to r-modes. Thus, the future possible detection of gravitational waves (due to unstable r-modes) from a star laying in the stable region of the frequency-temperature plane would be a strong indication for the existence of twin stars. Furthermore, we consider current data for the spin frequencies and temperatures of observed pulsars and compare them to the predictions made from equations of state employed in this study. We find that, depending on the transition density and the rigidness of the crust, hybrid equations of state may be a viable solution for the explanation of existing data.

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