Magnetized deformation of neutron stars

The high magnetic field in neutron stars leads to interesting consequences. One of them is the deformation of neutron stars. The correction equations due to deformation effect that complemented the spherical Tolmann-Oppenheimer-Volkoff equations can be calculated from Einstein field equations by including the magnetic contribution on the energy-momentum tensor of neutron star matter. Here, the multipole expansion is carried out on energy-momentum tensors containing magnetic fields as well as the corresponding metric around Schwarzschild one. The corresponding multipole expansions are performed only up to second order. We have shown that the effect of deformation appears more significantly in neutron stars with small masses. If we decrease the mass starting from maximum mass into the smaller one, the shape of neutron stars' changes from spherical into oblate.