Constant Mean Curvature Slices of the Reissner-Nordstr\"om 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 α 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\"om metric and the resultant slices will be investigated and then compared to those of the extended Schwarzschild solution.
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