Darmois matching and C3 matching
Abstract
We apply the Darmois and the C3 matching conditions to three different spherically symmetric spacetimes. The exterior spacetime is described by the Schwarzschild vacuum solution whereas for the interior counterpart we choose different perfect fluid solutions with the same symmetry. We show that Darmois matching conditions are satisfied in all three cases whereas the C3 conditions are not fulfilled. We argue that this difference is due to a non-physical behavior of the pressure on the matching surface.
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