Exact solutions of Einstein equations for anisotropic magnetic sources

Abstract

In this work, we have obtained exact solutions of Einstein equations for static and axially symmetric magnetized matter, specifically in plane-symmetric and almost-plane symmetric cases. Although these solutions impose constraints on the components of the energy-momentum tensor, some physically interesting situations, like the magnetized vacuum, might be described. Plane-symmetric solutions in presence of a non-vanishing cosmological constant have remarkable features. In particular, the system can be driven continuously to the isotropic case by an appropriate tuning of the cosmological constant, sweeping the magnetic field from weak to strong magnetic field regimes. The role of the cosmological constant in magnetic collapse is discussed with an emphasis in the description of jets from compact objects. For illustrative purposes, specific calculations for a magnetized electron gas have been developed.