Constant Mean Curvature Slices of the Reissner-Nordström Spacetime

Abstract: In order to specify a foliation of spacetime by spacelike hypersurfaces we need to place some restriction on the initial data and from this derive a way to calculate the lapse function $\alpha$ which measures the proper time and interval between neighbouring hypersurfaces along the normal direction. Here we study a prescribed slicing known as the Constant Mean Curvature (CMC) slicing. This slicing will be applied to the Reissner-Nordstr\"{o}m metric and the resultant slices will be investigated and then compared to those of the extended Schwarzschild solution.