Figure 1: Mass-radius relation of non-rotating and rotating white dwarfs. Taken from Becerra, et al. 2018, ApJ 857, 134.

The aim of this research is the construction of the white dwarf structure within a self-consistent description of the equation of state of the interior together with the solution of the hydrostatic equilibrium equations in general relativity. Non-magnetized, magnetized, non-rotating and rotating white dwarfs are studied. The interaction and evolution of a central white dwarf with a surrounding disk and magnetic fields, as occurred in the aftermath of white dwarf binary mergers, is also a subject of study.

Figure 2: Time evolution of the central temperature of a rotating white dwarf while losing angular momentum by magnetic-dipole radiation. Taken from Becerra, et al. 2019, MNRAS 487, 812.

We are interested in the astrophysical scenarios in which white dwarfs are present, either isolated or in binaries. Magnetized white dwarfs, soft gamma repeaters, anomalous X-ray pulsars, white dwarf pulsars, cataclysmic variables, binary white dwarf mergers, and type Ia supernovae are studied. The role of a realistic description of the white dwarf structure is emphasized.

Figure 3: Mass-equatorial radius relation of rotating neutron stars at the mass-shedding rate, for several up-to-date nuclear equations of state. Taken from Riahi, Kalantari and Rueda, 2019, PRD 99, 043004.

We study the properties of the neutron stars interiors and structure using realistic models of the nuclear matter equation of state within the general relativistic equations of equilibrium. Strong, weak, electromagnetic and gravitational interactions have to be jointly taken into due account within a self-consistent fully relativistic framework. Non-magnetized, magnetized, non-rotating and rotating neutron stars are studied.

Figure 4: Snapshots of the smoothed-particle-hydrodynamics (SPH) simulation of the induced gravitational collapse scenario for long gamma-ray bursts. Here we have a binary system formed by a carbon-oxygen star (CO_core), which explodes as supernova in presence of a 2M_⊙ companion neutron star. The accretion of supernova matter onto the NS induces the gravitational collapse of it into a black hole, with subsequent emission of a gamma-ray burst. The system has an initial orbital period of 5 min. The plots show the mass density on the binary equatorial plane, at different times of the simulation. Taken from Becerra, et al., 2019, ApJ 871, 14.

We study astrophysical scenarios harboring neutron stars such as isolated and binary pulsars, low and intermediate X-ray binaries, inspiraling and merging double neutron stars. Most extreme cataclysmic events involving neutron stars and their role in the explanation of extraordinarily energetic astrophysical events such as gamma-ray bursts are analyzed in detail.

Figure 5: Snapshots of the time evolution of 0.8 + 0.6 M_⊙ white-dwarf binary merger. The simulation uses the SPH technique with 7×10⁵ particles. The newly-formed central white dwarf has approximately 1.1 M_⊙. In the sequence it can be seen how the secondary star is disrupted by Roche lobe overflow. Little mass is ejected, in the present simulation nearly 1.2 × 10⁻³ M_⊙. Taken from Rueda, et al., 2019, JCAP 3, 044.

We here study the possible radiation mechanisms of white dwarfs and neutron stars. We are thus interested in the electromagnetic, neutrino and gravitational wave emission at work in astrophysical systems such as compact star magnetosphere, accretion disks surrounding them and inspiraling and merging relativistic binaries such as double neutron stars, neutron star-white dwarfs, white dwarf-white dwarf and neutron star-black hole.

Figure 6: Electric and magnetic field lines of the solution of the Einstein-Maxwell equations by Wald 1974: an asymptotically uniform magnetic field, aligned with the rotation axis of a Kerr black hole. The blue lines show the magnetic field lines and the violet show the electric field lines. This electromagnetic field structure has been exploited in a new electrodynamical process to extract the rotational of a Kerr black hole that explains the high-energy GeV-TeV emission from gamma-ray bursts. Taken from Ruffini, et al., 2019, ApJ 886, 82.

We analyze the ability of analytic exact solutions of the Einstein and Einstein-Maxwell equations to describe the exterior spacetime of compact stars such as white dwarfs and neutron stars. For this we compare and contrast exact analytic with numerical solutions of the stationary axisymmetric Einstein equations. The problem of matching between interior and exterior spacetime is addressed in detail. The effect of the quadrupole moment on the properties of the spacetime is also investigated. Particular attention is given to the application of exact solutions in astrophysics, e.g. the dynamics of particles around compact stars and its relevance in astrophysical systems such as X-ray binaries and gamma-ray bursts.