The recent analysis on the central compact object in the HESS J1731-347 remnant suggests interestingly small values for its mass and radius. Such an observation favors soft nuclear models that may be challenged by the observation of massive compact stars. In contrast, the recent PREX-II experiment, concerning the neutron skin thickness of ${}^{208}\mathrm{Pb}$, points toward stiff equations of state that favor larger compact star radii. In the present study, we aim to explore the compatibility between stiff hadronic equations of state (favored by PREX-II) and the HESS J1731-347 remnant in the context of hybrid stars. For the construction of hybrid equations of state we use three widely employed Skyrme models combined with the well-known vector MIT bag model. Furthermore we consider two different scenarios concerning the energy density of the bag. In the first case, that of a constant bag parameter, we find that the resulting hybrid equations of state (which satisfy the HESS J1731-347 constraints) are strongly disfavored by the observation of $\sim 2M_{\odot }$ pulsars. However, the introduction of a Gaussian density dependence yields results that are compatible with the conservative $2M_{\odot }$ constraint. The utilization of recent data based on the observation of PSR $\mathrm{J}0030+0451$, PSR J0952-0607, and GW190814 allows for the imposition of additional constraints on the relevant parameters and the stiffness of the two phases. Interestingly, we find that the derived hybrid equations of state do not satisfy the PSR $\mathrm{J}0030+0451$ constraints in $1\sigma$ and only marginally agree with the $2\sigma$ estimations. In addition, we estimate that the observation of massive pulsars, like PSR J0952-0607, in combination with the existence of HESS J1731-347, may require a strong phase transition below $\sim 1.7n_0$. Finally, we show that the supermassive compact object ($2.5-2.67M_{\odot }$) involved in GW190814 could potentially be explained as a rapidly rotating hybrid star.

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.

The observation and distinction of two compact stars with an identical mass but a 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 appearing in the $r$-mode instability windows and spin-down evolution of twin stars. We conclude that two stars with an 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.

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.