Slowly rotating charged fluid balls and their matching to an exterior domain

TL;DR

This paper extends the slow-rotation approximation to charged fluid balls, matching interior solutions to exterior Reissner-Nordstrom spacetime, and investigates conditions for asymptotic flatness, providing new insights into charged rotating bodies in general relativity.

Contribution

It develops a charged generalization of the Hartle slow-rotation approximation and proves a theorem relating magnetic field parameters to asymptotic flatness.

Findings

Exterior region is asymptotically flat iff external magnetic field parameter vanishes.

The Garcia solution's magnetic parameter C_2 is explicitly determined.

Numerical analysis supports the conjecture that Garcia metric cannot match an asymptotically flat exterior.

Abstract

The slow-rotation approximation of Hartle is developed to a setting where a charged rotating fluid is present. The linearized Einstein-Maxwell equations are solved on the background of the Reissner-Nordstrom space-time in the exterior electrovacuum region. The theory is put to action for the charged generalization of the Wahlquist solution found by Garcia. The Garcia solution is transformed to coordinates suitable for the matching and expanded in powers of the angular velocity. The two domains are then matched along the zero pressure surface using the Darmois-Israel procedure. We prove a theorem to the effect that the exterior region is asymptotically flat if and only if the parameter C_{2}, characterizing the magnitude of an external magnetic field, vanishes. We obtain the form of the constant C_{2} for the Garcia solution. We conjecture that the Garcia metric cannot be matched to an asymptotically flat exterior electrovacuum region even to first order in the angular velocity. This conjecture is supported by a high precision numerical analysis.