Darmois matching and $C^3$ matching

Abstract

We apply the Darmois and the $C^3$ 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 $C^3$ conditions are not fulfilled. We argue that this difference is due to a non-physical behavior of the pressure on the matching surface.

arXiv commentReplaced with the version matching the published one in CQG

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• Physical Acceptability of Isolated, Static, Spherically Symmetric, Perfect Fluid Solutions of Einstein's Equations
• Characterizing repulsive gravity with curvature eigenvalues
• Revisiting the Darmois and Lichnerowicz junction conditions
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• $C^3$ matching for asymptotically flat spacetimes
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Cited by in corpus (1)

• Fermi-normal coordinates for the Newtonian approximation of gravity