Matching conditions for the interior and exterior spacetimes of astrophysical compact objects
AbstractWe study the problem of matching the interior and exterior solutions of Einstein’s equations for astrophysical compact objects. 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. We propose a C3 matching which consists in demanding that the derivatives of a particular curvature eigenvalue are smooth on the matching hypersurface. 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. As aresult we obtain a minimum radius at which the matching can be carried out and a fixed value for the pressure on the symmetry axis. These values are then used to reach the smooth matching of the interior and exterior metric functions. Several perfect fluid solutions in Newton gravity are tested.
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