General Relativistic Effects on Multipole Magnetic Field Evolution in Neutron Stars: Implications for High‐Braking‐Index Magnetars

ABSTRACT Neutron stars, particularly magnetars, exhibit extreme physical conditions with some of the strongest magnetic fields in the universe. Understanding the evolution of these magnetic fields is crucial for interpreting their observed properties, such as high braking indices and X‐ray emissions. In this work, we investigate the decay of multipole magnetic fields in neutron stars by incorporating general relativistic (GR) effects into the induction equations. We derive GR‐corrected evolution equations for dipole (), quadrupole (), and octupole () fields, considering both toroidal and poloidal components. Our calculations show that GR effects significantly extend the magnetic field decay timescales, with the redshift factor for a typical neutron star. We find that the GR‐corrected decay timescales better align with observed characteristics of magnetars. Additionally, we discuss the implications of our model for X‐ray emissions and magnetic energy release rates in magnetars. Our results highlight the importance of GR corrections for accurate predictions of magnetic field evolution and related observational phenomena.