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In this work, we study the properties of magnetized white dwarfs taking intoaccount possible instabilities due to electron capture and pycnonuclear fusionreactions in the cores of such objects. The structure of white dwarfs isobtained by solving the Einstein-Maxwell equations with a poloidal magneticfield in a fully general relativistic approach. The stellar interior iscomposed of a regular crystal lattice made of carbon ions immersed in adegenerate relativistic electron gas. The onsets of electron capture reactionsand pycnonuclear reactions are determined with and without magnetic fields. Wefind that magnetized white dwarfs violate the standard Chandrasekhar mass limitsignificantly, even when electron capture and pycnonuclear fusion reactions arepresent in the stellar interior. We obtain a maximum white dwarf mass of around$2.14\,M_{\odot}$ for a central magnetic field of $\sim 3.85\times 10^{14}$~G,which indicates that magnetized white dwarfs may play a role for theinterpretation of superluminous type Ia supernovae. Furthermore, we show thatthe critical density for pycnonuclear fusion reactions limits the central whitedwarf density to $9.35\times 10^9$ g/cm$^3$. As a result, equatorial radii ofwhite dwarfs cannot be smaller than $\sim 1100$~km. Another interesting featureconcerns the relationship between the central stellar density and the strengthof the magnetic field at the core of a magnetized white dwarf. For highmagnetic fields, we find that the central density increases (stellar radiusdecrease) with magnetic field strength, which makes ultramagnetized whitedwarfs more compact. The opposite is the case, however, if the central magneticfield is less than $\sim 10^{13}$~G. In the latter case, the central densitydecreases (stellar radius increases) with central magnetic field strengths.

Very Magnetized White Dwarfs with Axisymmetric Magnetic Field and the  Importance of the Electron Capture and Pycnonuclear Fusion Reactions for  their Stability