General Relativistic Razor-Thin Disks with Magnetically Polarized Matter
  The origin of magnetic fields in the universe still remains unknown and
constitutes one of the most intriguing questions in astronomy and astrophysics.
Their significance is enormous since they have a strong influence on many
astrophysical phenomena. In regards of this motivation, theoretical models of
galactic disks with sources of magnetic field may contribute to understand the
physics behind them. Inspired by this, we present a new family of analytical
models for thin disks composed by magnetized material. The solutions are
axially symmetric, conformastatic and are obtained by solving the
Einstein-Maxwell Field Equations for continuum media without the test field
approximation, and assuming that the sources are razor-thin disk of
magnetically polarized matter. We find analytical expressions for the surface
energy density, the pressure, the polarization vector, the electromagnetic
fields, the mass and the rotational velocity for circular orbits, for two
particular solutions. In each case, the energy-momentum tensor agrees with the
energy conditions and also the convergence of the mass for all the solutions is
proved. Since the solutions are well-behaved, they may be used to model
astrophysical thin disks, and also may contribute as initial data in numerical
simulations. In addition, the process to obtain the solutions is described in
detail, which may be used as a guide to find solutions with magnetized material
in General Relativity.
