The Feynman-Metropolis-Teller treatment of compressed atoms has been recently generalized to relativistic regimes and applied to the description of static and rotating white dwarfs in general relativity. We present here the extension of this treatment to the case of finite temperatures and construct the corresponding equation of state (EOS) of the system; applicable in a wide regime of densities that includes both white dwarfs and neutron star outer crusts. We construct the massradius relation of white dwarfs at finite temperatures obeying this new EOS and apply it to the analysis of ultra low-mass white dwarfs with M 0.2M⊙. In particular, we analyze the case of the white dwarf companion of PSR J1738+0333. The formulation is then extrapolated to compressed nuclear matter cores of stellar dimensions, systems with mass numbers A ≈ (m Planck /mn) 3 or mass Mcore ≈ M⊙, where m Planck and mn are the Planck and the nucleon mass. For T ≪ mec 2 /kB ≈ 5.9 × 10 9 K, a family of equilibrium configurations can be obtained with analytic solutions of the ultra-relativistic Thomas-Fermi equation at finite temperatures. Such configurations fulfill global but not local charge neutrality and have strong electric fields on the core surface. We find that the maximum electric field at the core surface is enhanced at finite temperatures with respect to the degenerate case.

We study the thermal evolution of neutron stars containing deconfined quark matter in their core. Such objects are generally referred to as quark-hybrid stars. The confined hadronic matter in their core is described in the framework of non-linear relativistic nuclear field theory. For the quark phase we use a non-local extension of the SU(3) Nambu Jona-Lasinio model with vector interactions. The Gibbs condition is used to model phase equilibrium between confined hadronic matter and deconfined quark matter. Our study indicates that high-mass neutron stars may contain between 35 and 40% deconfined quark-hybrid matter in their cores. Neutron stars with canonical masses of around 1.4 M⊙ would not contain deconfined quark matter. The central proton fractions of the stars are found to be high, enabling them to cool rapidly. Very good agreement with the temperature evolution established for the neutron star in Cassiopeia A (Cas A) is obtained for one of our models (based on the popular NL3 nuclear parametrization), if the protons in the core of our stellar models are strongly paired, the repulsion among the quarks is mildly repulsive, and the mass of Cas A has a canonical value of 1.4 M⊙.

There is solid observational evidence on the existence of massive, M ∼ 1 M , highly magnetized white dwarfs (WDs) with surface magnetic fields up to B ∼ 10 9 G. We show that, if in addition to these features, the star is fast rotating, it can become a rotation-powered pulsar-like WD and emit detectable high-energy radiation. We infer the values of the structure parameters (mass, radius, moment of inertia), magnetic field, rotation period and spin-down rates of a WD pulsar death-line. We show that WDs above the death-line emit blackbody radiation in the soft X-ray band via the magnetic polar cap heating by back flowing pair-created particle bombardment and discuss as an example the X-ray emission of soft gamma-repeaters and anomalous X-ray pulsars within the WD model.