C3 matching for asymptotically flat spacetimes

Abstract

We propose a criterion for finding the minimum distance at which an interior solution of Einstein’s equations can be matched with an exterior asymptotically flat solution. The location of the matching hypersurface is thus constrained by a criterion defined in terms of the eigenvalues of the Riemann curvature tensor by using repulsive gravity effects. To determine the location of the matching hypersurface, we use the first derivatives of the curvature eigenvalues, implying C3 differentiability conditions. The matching itself is performed by demanding continuity of the curvature eigenvalues across the matching surface. We apply the C3 matching approach to spherically symmetric perfect fluid spacetimes and obtain the physically meaningful condition that density and pressure should vanish on the matching surface. Several perfect fluid solutions in Newton and Einstein gravity are tested.