In this work we study the effects of strong magnetic fields on hybrid stars by using a full generalrelativity approach, solving the coupled Maxwell-Einstein equation in a self-consistent way. The magnetic field is assumed to be axi-symmetric and poloidal. We take into consideration the anisotropy of the energy-momentum tensor due to the magnetic field, magnetic field effects on equation of state, the interaction between matter and the magnetic field (magnetization), and the anomalous magnetic moment of the hadrons. The equation of state used is an extended hadronic and quark SU(3) non-linear realization of the sigma model that describes magnetized hybrid stars containing nucleons, hyperons and quarks. According to our results, the effects of the magnetization and the magnetic field on the EoS do not play an important role on global properties of these stars. On the other hand, the magnetic field causes the central density in these objects to be reduced, inducing major changes in the populated degrees of freedom and, potentially, converting a hybrid star into a hadronic star.

In this work we compute models for relativistic white dwarfs in the presence of strong magnetic fields. These models possibly contribute to super-luminous SNIa. With an assumed axi-symmetric and poloidal magnetic field, we study the possibility of existence of super-Chandrasekhar magnetized white dwarfs by solving numerically the Einstein-Maxwell equations, by means of a pseudo-spectral method. We obtain a self-consistent rotating and non-rotating magnetized white dwarf models. According to our results, a maximum mass for a static magnetized white dwarf is 2.13 $\rm{M_{\odot}}$ in the Newtonian case and 2.09 $\rm{M_{\odot}}$ while taking into account general relativistic effects. Furthermore, we present results for rotating magnetized white dwarfs. The maximum magnetic field strength reached at the center of white dwarfs is of the order of $10^{15}\,$G in the static case, whereas for magnetized white dwarfs, rotating with the Keplerian angular velocity, is of the order of $10^{14}\,$G

The quark gluon plasma (QGP) at zero temperature and high baryon number is a system that may be present inside compact stars. It is quite possible that this cold QGP shares some relevant features with the hot QGP observed in heavy ion collisions, being also a strongly interacting system. In a previous work we have derived from the QCD Lagrangian an equation of state (EOS) for the cold QGP, which can be considered an improved version of the MIT bag-model EOS. Compared to the latter, our EOS reaches higher values of the pressure at comparable baryon densities. This feature is due to perturbative corrections and also to nonperturbative effects. Here we apply this EOS to the study of neutron stars, discussing the absolute stability of quark matter and computing the mass-radius relation for self-bound (strange) stars. The maximum masses of the sequences exceed two solar masses, in agreement with the recently measured values of the mass of the pulsar PSR J1614-2230, and the corresponding radii of around 10-11 km.

The presence of quark-hadron phase transitions in neutron stars can be related to several interesting phenomena. In particular, previous calculations have shown that fast rotating neutron stars, when subjected to a quark-hadron phase transition in their interiors, could give rise to the backbending phenomenon characterized by a spin-up era. In this work, we use an equation of state composed of two phases, containing nucleons (and leptons) and quarks. The hadronic phase is described in a relativistic mean field formalism that takes many-body forces into account, and the quark phase is described by the MIT bag model with a vector interaction. Stationary and axisymmetric stellar models are obtained in a self-consistent way by solving numerically the Einstein-Maxwell equations by means of a pseudo-spectral method. As a result, we obtain the interesting backbending phenomenon for fast spinning neutron stars. More importantly, we show that a magnetic field, which is assumed to be axi-symmetric and poloidal, can also be enhanced due to the phase transition from normal hadronic matter to quark matter on highly magnetized neutron stars. Therefore, in parallel to the spin-up era, classes of neutron stars endowed with strong magnetic fields may go through a "magnetic-up era" in their lives.

In this Letter, we report a realistic calculation of the magnetic field profile for the equation of state inside strongly magnetized neutron stars. Unlike previous estimates, which are widely used in the literature, we find that magnetic fields increase relatively slowly with increasing baryon chemical potential (or baryon density) of magnetized matter. More precisely, the increase is polynomial instead of exponential, as previously assumed. Through the analysis of several different realistic models for the microscopic description of stellar matter (including hadronic, hybrid and quark models) combined with general relativistic solutions endowed with a poloidal magnetic field obtained by solving Einstein-Maxwell's field equations in a self-consistent way, we generate a phenomenological fit for the magnetic field distribution in the stellar polar direction to be used as input in microscopic calculations.