Investigating the rigidly rotating disc of dust with constant specific charge, we find that it leads to an extreme Kerr-Newman black hole in the ultrarelativistic limit. A necessary and sufficient condition for a black hole limit is, that the electric potential in the co-rotating frame is constant on the disc. In that case certain other relations follow. These relations are reviewed with a highly accurate post-Newtonian expansion.Remarkably it is possible to survey the leading order behaviour close to the black hole limit with the post-Newtonian expansion. We find that the disc solution close to that limit can be approximated very well by a "hyperextreme" Kerr-Newman solution with the same gravitational mass, angular momentum and charge.

We present an algorithm for obtaining the post-Newtonian expansion of the asymptotically flat solution to the Einstein-Maxwell equations describing a rigidly rotating disc of dust with a constant specific charge. Explicit analytic expressions are calculated up to the eighth order. The results are used for a physical discussion of the extreme relativistic limiting cases. We identify strong evidence for a transition to an extreme Kerr-Newman black hole.

We present the foundations of a new solution technique for the characteristic initial value problem (IVP) of colliding plane gravitational waves. It has extensive similarities to the approach of Alekseev and Griffiths in 2001, but we use an inverse scattering method with a Riemann-Hilbert problem (RHP), which allows for a transformation to a continuous RHP with a solution given in terms of integral equations for non-singular functions. Ambiguities in this procedure lead to the construction of a family of spacetimes containing the solution to the IVP. Therefore the described technique also serves as an interesting solution generating method. The procedure is exemplified by extending the Szekeres class of colliding wave spacetimes with 2 additional real parameters. The obtained solution seems to feature a limiting case of a new type of impulsive waves, which are circularly polarised.If we choose λ K u so that |Λ K (λ 1 )| 2 = (L 2 (λ 1 )) x K 2 , the unitarisation transformation applied after removing the discontinuities at ±λ 2 yieldŝ(106) Hence the unitarisation transformation reproduces the initial settings at ±λ 1 withĜ K J still Lipschitz continuous at these points. FurthermoreĜ K J = 1 almost everywhere on Γ and so the matrix solutionΦ is no longer described by a single expression for both sides of the contour. With (λ K u ) > 0 we assure that Λ K has neither zeros nor poles. The full transformation formulaWe can now diagonalise the jump matrixĜ K J at ±λ 1 by the rotation transformation G

We analyse the response of laser interferometric gravitational wave detectors using the full Maxwell equations in curved spacetime in the presence of weak gravitational waves. Existence and uniqueness of solutions is ensured by setting up a suitable boundary value problem. This puts on solid ground previous approximate calculations. We find consistency with previous results obtained from eikonal expansions at the level of accuracy accessible to current gravitational wave detectors.

Some previously published expressions for the perturbation of light by gravitational waves exhibit pathological behaviour in the limit of parallel propagation. We show that this is caused by similarly pathological initial or boundary data and can thus be remedied by implementing better-behaved initial conditions.