Abstract We revisit the problem of the maximum masses of magnetized white dwarfs (WDs). The impact of a strong magnetic field on the structure equations is addressed. The pressures become anisotropic due to the presence of the magnetic field and split into parallel and perpendicular components. We first construct stable solutions of the Tolman-Oppenheimer-Volkoff equations for parallel pressures and find that physical solutions vanish for the perpendicular pressure when B ≿1013 G. This fact establishes an upper bound for a magnetic field and the stability of the configurations in the (quasi) spherical approximation. Our findings also indicate that it is not possible to obtain stable magnetized WDs with super-Chandrasekhar masses because the values of the magnetic field needed for them are higher than this bound. To proceed into the anisotropic regime, we can apply results for structure equations appropriate for a cylindrical metric with anisotropic pressures that were derived in our previous work. From the solutions of the structure equations in cylindrical symmetry we have confirmed the same bound for B ~ 1013 G, since beyond this value no physical solutions are possible. Our tentative conclusion is that massive WDs with masses well beyond the Chandrasekhar limit do not constitute stable solutions and should not exist.
Keywords magnetic fields — white dwarfs — equation of state
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