## Some aspects of strong gravity effects on the electromagnetic field of a radio pulsar magnetosphere : solving the Maxwell’s equations.

##### Abstract

The general relativistic (GR) effects of a neutron star play a substantial role on the physics
at the stellar surface. These neutron stars also host a very strong magnetic field and spin
with periods of a few seconds to as high as milliseconds. In order to account for the
motion of charged particles in the magnetosphere immediately outside the stellar surface,
it is essential to include the GR effects in the Maxwell’s equations. To account for the
frame dragging effects due to the stellar spin, we have, in this dissertation, considered a
3+1 decomposition of the spacetime and applied them to find the solutions to Maxwell’s
equations of an isolated neutron star in a vacuum, for different cases. In order to derive our
solutions we made use of the vector spherical harmonics in a curved spacetime. We first
considered an aligned dipole magnetic field from which we formed a general formalism for
the magnetic and electric fields for higher orders. We then considered an orthogonal dipole
magnetic field for which we solved only for the non-rotating case. In a realistic scenario
for a radio pulsar, the radio beams which originate from the pole caps of the magnetic
field, have a finite angle with the spin axis and hence it is necessary to find a model for
an oblique rotator. This study will be helpful in the future for the understanding of the
charged particle interaction at the pulsar pole caps and hence for the emission mechanism
of a radio pulsar.