Abstract
The stellar magnetic field configuration and solutions of Maxwell equations in the external background spacetime of a magnetized spherical stars in the Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity and in modified $f(R)$ gravity are studied. The star is modeled as a sphere consisting of perfect highly magnetized fluid with infinite conductivity and frozen-in magnetic field. With respect to solutions for magnetic fields found in the Schwarzschild spacetime star in modified gravity theories, enhancing corrections are added to the exterior magnetic field. The energy losses through magnetodipolar radiation of the rotating magnetized compact star within alternative gravity theories is also considered. The question of whether these models can be considered as an alternative theory for general relativity is also discussed through astrophysical application of the obtained magnetodipolar energy loss formula. Finally we analyze the role of general relativistic effect on the decay of a neutron star's magnetic field in modified theories of gravity.
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