Introduction.

The understanding of the composition and macroscopic properties of compact objects is one of the biggest challenges of Astrophysics. In particular, if the object is magnetized, one faces the still unsolved problem of finding the structure of a non-spherical star. Following our studies on these topics, here we present a set of structure equations for spheroidal compact objects, as long as they are not too far from the spherical shape.

Methods.

These equations describe any compact object whose equation of state has magnetic anisotropy, and have been successfully applied to the study of magnetized White Dwarfs, Bose-Einstein condensate Stars and Strange Stars.

Results and Discussion.

As collateral results, we obtained solutions to Einstein’s equations suitable for describing the magnetosphere of compact objects, and performed a preliminary study of a model for astrophysical jets.

Conclusions.

From these studies, we show that a uniform magnetic field does not increase the maximum mass of compact objects, its biggest effect being their deformation. In addition, we proposed and validated a mechanism for the generation of the stellar magnetic field, which constitutes one of the major novelties of the work, and found that the stars of intermediate masses are the candidates to produce the most intense gravitational waves.

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