Pulsar magnetospheres: a general relativistic treatment

A fully general relativistic description of pulsar magnetospheres is provided. To be more specific, a study of pulsar magnetospheres is performed in the context of general relativistic magnetohydrodynamics (MHD) employing the so-called Grad-Shafranov approach. Not surprisingly, the resulting Grad-Shafranov equations and all the other related general relativistic MHD equations turn out to take essentially the same structures as those for a (rotating) black hole magnetosphere. Other different natures between the two cases including the structure of singular surfaces of MHD flows in each magnetosphere are essentially encoded in the different space-time (metric) contents. In this way, pulsar and black hole magnetospheres can be described in a unified fashion. Particularly, the direction of poloidal currents circulating in the neutron star magnetosphere turns out to be the same as that of currents circulating in a black hole magnetosphere, which in turn leads to pulsar and black hole spin-down via 'magnetic braking'.