On the Einstein-Maxwell equations for a 'stiff' membrane

The Einstein-Maxwell equations are examined for a distributional stress tensor depending on the mean shape of an immersion in a manifold with a piecewise smooth metric tensor. A solution is discussed that matches an exterior Reissner-Nordstroem metric to an interior Minkowski metric. Such a solution extends the Dirac particle model to incorporate both gravitational and electromagnetic interactions. (author)