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In this study, we estimate the mass density thresholds for the onset of electron capture reactions and pycnonuclear fusion reactions in the cores of fast, massive and highly magnetized white dwarfs and white dwarf pulsars and discuss the impact of microscopic stability and rapid rotation on the structure and stability of such objects. We find that fast rotation increases the mass of a WD by up to 10%, while the central density may drop by one to two orders of magnitude, depending on stellar mass and rate of rotation. We also note that the central densities of the rotating WDs are smaller than those of the non-rotating stars, since less pressure is to be provided by the nuclear equation of state in the rotating case, and that the maximum-mass limit slightly decreases when lattice contributions are taken into account, which soften the equation of state mildly. This softening leads to white dwarfs with somewhat smaller radii and therefore smaller Kepler periods. Overall, we find that very massive and magnetic 12C +16O white dwarfs have rotational Kepler periods on the order of 0.5 seconds. Pycnonuclear reactions are triggered in these white dwarfs at masses that are markedly smaller than the maximum white-dwarf masses. The corresponding rotational periods turn out to be in the 5 second (around 2 Hz) range 

We review the covariant density functional approach to the equation of state of the dense nuclear matter in compact stars. The main emphasis is on the hyperonization of the dense matter, and the role played by the Delta-resonance. The implications of hyperonization for the astrophysics of compact stars, including the equation of state, composition, and stellar parameters are examined. The mass-radius relation and tidal deformabilities of static and rapidly rotating (Keplerian) configurations are discussed in detail. We briefly touch upon some other recent developments involving hyperonization in hot hypernuclear matter at high- and low-densities.