General relativistic effects of gravitomagnetic charge on pulsar magnetospheres and particle acceleration in the polar cap

We study the magnetospheric structure surrounding a rotating, magnetized neutron star with nonvanishing NUT (Newman-Unti-Tamburino) parameter. For simplicity, the Goldreich-Julian charge density is analyzed for an aligned neutron star, with zero inclination between magnetic field, gravitomagnetic field, and rotation axis. From the system of Maxwell's equations in the spacetime of a slowly rotating NUT star, a second-order differential equation for the electrostatic potential is derived. The analytical solution of this equation indicates a general relativistic modification of the accelerating electric field and charge density along the open field lines due to the gravitomagnetic charge. The implications of this effect for the magnetospheric energy-loss problem are highlighted. We also derive the equations of motion for a test particle in the magnetosphere of a slowly rotating NUT star. Then we analyze particle motion in the polar cap and show that the NUT parameter can significantly change the conditions for particle acceleration.