In this work , we study the properties of magnetized white dwarfs taking into account possible instabilities due to electron capture and pycnonuclear fusion reactions in the cores of such objects .
The structure of white dwarfs is obtained by solving the Einstein-Maxwell equations with a poloidal magnetic field in a fully general relativistic approach .
The stellar interior is composed of a regular crystal lattice made of carbon ions immersed in a degenerate relativistic electron gas .
The onsets of electron capture reactions and pycnonuclear reactions are determined with and without magnetic fields .
We find that magnetized white dwarfs violate the standard Chandrasekhar mass limit significantly , even when electron capture and pycnonuclear fusion reactions are present 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 the interpretation of superluminous type Ia supernovae .
Furthermore , we show that the critical density for pycnonuclear fusion reactions limits the central white dwarf density to 9.35 \times 10 ^ { 9 } g/cm ^ { 3 } .
As a result , equatorial radii of white dwarfs can not be smaller than \sim 1100 km .
Another interesting feature concerns the relationship between the central stellar density and the strength of the magnetic field at the core of a magnetized white dwarf .
For high magnetic fields , we find that the central density increases ( stellar radius decrease ) with magnetic field strength , which makes ultramagnetized white dwarfs more compact .
The opposite is the case , however , if the central magnetic field is less than \sim 10 ^ { 13 } G. In the latter case , the central density decreases ( stellar radius increases ) with central magnetic field strengths .