General relativistic corrections to the pulsar spin-down luminosity

Pulsar magnetospheres are typically modeled in flat spacetime. Adopting our new method for smoothly matching general relativistic ideal magnetohydrodynamics to its force-free limit, we perform the first systematic study of pulsar magnetospheres in general relativity. We endow the neutron star with a general relativistic dipole magnetic field, and model the dense interior with ideal magnetohydrodynamics, and assume force-free electrodynamics in the exterior. Normalizing the spin-down luminosity by its corresponding Minkwoski value, we find that relativistic effects give rise to a modest enhancement: the maximum enhancement for $n=1$ polytropes is $\sim 23\%$, and for a rapidly rotating $n=0.5$ polytrope we find an enhancement of $\sim 35\%$. We expect stiffer equation of state and more rapidly rotating neutron stars to lead to even larger enhancements in the spin-down luminosity.