Introduction

Introduction

Pulsars are believed to be rapidly rotating neutron stars that lose their rotational kinetic energy primarily due to emission of electromagnetic radiation. Pulsars are extremely accurate clocks that can be used to probe fundamental physics, such as the nuclear equation of state (EOS), and theories of gravity. They even function as emitters of gravitational waves.

The light cylinder around a pulsar marks the location between a near and a far radiation zone. In the near zone, the pulsar magnetosphere corotates with the star. The magnetic field lines return to the stellar surface. In the far zone, the magnetic lines are open and extend to infinity; the open lines contribute to an outgoing Poynting flux of electromagnetic radiation.

The magnetic fields are evolved via the ideal GRMHD equations and, in the exterior, its force-free (GRFF) limit. The force-free dynamical variables we adopt are the magnetic field (B) and Poynting vector (S) under the constraints S·B=0 and S² < B². The evolution equations for these dynamical varibles are written as a set of conservation laws precisely in the same form as the ideal GRMHD evolution equations, so that the same GRMHD infrastructure can be adopted to solve both the ideal MHD and the FFE equations.

We initially seed the NS with a purely poloidal magnetic field that gives rise to a dipole in the exterior.