We investigate the use of hybrid equations of state in binary neutron-star simulations in full general relativity, where thermal effects are included in an approximate way through the adiabatic index Γ th . We employ a newly developed finite-temperature equation of state derived in the Brueckner-Hartree-Fock approach and carry out comparisons with the corresponding hybrid versions of the same equation of state, investigating how different choices of Γ th affect the gravitational-wave signal and the hydrodynamical properties of the remnant. We also perform comparisons with the widely used SFHo equation of state, detailing the differences between the two cases. Overall, we determine that when using a hybrid equation of state in binary neutron-star simulations, the value of thermal adiabatic index Γ th ≈ 1.7 best approximates the dynamical and thermodynamical behaviour of matter computed using complete, finite-temperature equations of state.

We calculate neutron star's moment of inertia and deformabilities using various microscopic equations of state for nuclear and hybrid star configurations. We confirm several universal relations between the various observables in these cases. We focus in particular on the constraints for the neutron star radii imposed by a determination of the average tidal deformability of the binary neutron star system GW170817. We find compatible radii between 12 and 13 kilometers and identify the suitable equations of state.

We study the properties of hot beta-stable nuclear matter using equations of state derived within the Brueckner-Hartree-Fock approach at finite temperature including consistent three-body forces. Simple and accurate parametrizations of the finite-temperature equations of state are provided. The properties of hot neutron stars are then investigated within this framework, in particular the temperature dependence of the maximum mass. We find very small temperature effects and analyze the interplay of the different contributions.

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