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arXiv · 1205.0500

Matching conditions in relativistic astrophysics

Hernando Quevedo
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Abstract

We present an exact electrovacuum solution of Einstein-Maxwell equations with infinite sets of multipole moments which can be used to describe the exterior gravitational field of a rotating charged mass distribution. We show that in the special case of a slowly rotating and slightly deformed body, the exterior solution can be matched to an interior solution belonging to the Hartle-Thorne family of approximate solutions. To search for exact interior solutions, we propose to use the derivatives of the curvature eigenvalues to formulate a $C^3-$matching condition from which the minimum radius can be derived at which the matching of interior and exterior spacetimes can be carried out. We prove the validity of the $C^3-$matching in the particular case of a static mass with a quadrupole moment. The corresponding interior solution is obtained numerically and the matching with the exterior solution gives as a result the minimum radius of the mass configuration.

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Hernando Quevedo. 2012-05-02. Matching conditions in relativistic astrophysics. https://doi.org/10.1142/9789814374552_0003

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