General Relativistic Electromagnetism and Particle Acceleration in a Pulsar Polar Cap

We reconstruct a 3 + 1 formalism of general relativistic electromagnetism and derive the equations of motion of charged particles in a pulsar magnetosphere, taking account of the inclination between the rotation axis and the magnetic axis. Unlike previous works in which space charge is evaluated by assuming the flow velocity to be light speed, we analyze particle motion in the polar cap, finding that gravity significantly changes its dynamics and the condition for acceleration.