Matching conditions in relativistic astrophysics

TL;DR

This paper develops an exact Einstein-Maxwell solution with multipole moments for rotating charged bodies, proposes a new $C^3$-matching condition for interior-exterior spacetime matching, and applies it to static quadrupole cases.

Contribution

It introduces a novel $C^3$-matching method based on curvature eigenvalues derivatives for interior-exterior spacetime matching in relativistic astrophysics.

Findings

Derived an exact electrovacuum solution with multipole moments.

Proved the $C^3$-matching condition for static quadrupole cases.

Numerically obtained interior solutions and minimum matching radius.

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.