On the existence of the field line solutions of the Einstein-Maxwell
  equations
  The main result of this paper is the proof that there are local electric and
magnetic field configurations expressed in terms of field lines on an arbitrary
hyperbolic manifold. This electromagnetic field is described by (dual)
solutions of the Maxwell's equations of the Einstein-Maxwell theory. These
solutions have the following important properties: i) they are general, in the
sense that the knot solutions are particular cases of them and ii) they reduce
to the electromagnetic fields in the field line representation in the flat
space-time. Also, we discuss briefly the real representation of these
electromagnetic configurations and write down the corresponding Einstein
equations.
