Rotating Einstein--Maxwell fields: smoothly matched exterior and interior spacetimes with charged dust and surface layer

Abstract

We obtain exact exterior and matching interior stationary axially symmetric solutions of the Einstein--Maxwell field equations, for rigidly rotating charged dust with vanishing Lorentz force. The solutions generate two sources, an infinitely long cylinder of charged dust rigidly rotating about its axis, and a surface layer with surface 4-current located on a singular hypersurface perpendicular to the axis of the cylinder at the origin of the coordinate system. The surface layer extends from the interior of the cylinder to the exterior, but the physical components of its surface stress--energy tensor and surface 4-current, vanish at infinite radial distances on the hypersurface, in any direction away from the origin. The mass and charge densities of the cylinder, also vanish at infinite distances away from either side of the hypersurface. The solutions are physically significant, because both sources of spacetime represent physically reasonable matter with well defined matter, electromagnetic and surface stress--energy tensors, whose physical components vanish at spatial infinity. The junction conditions on the hypersurface separating the exterior from the interior spacetime, and the more complicated set of junction conditions on the singular hypersurface, are satisfied. An analysis by means of the physical components of the Riemann curvature tensor, shows that there are no singularities on the rotation axis and that spacetime is asymptotically flat everywhere at spatial infinity. An addendum to this article has been published in 1996 Class. Quantum Grav. 13 791-7.