Timelike Geodesic Currents in the Stationary, Axisymmetric, Force-free Magnetosphere of a Kerr Black Hole

TL;DR

This paper analytically investigates geodesic currents in the magnetosphere of a Kerr black hole, focusing on energy extraction via matter currents and their compliance with the Znajek condition.

Contribution

It provides a detailed analytical study of geodesic currents in Kerr black hole magnetospheres, emphasizing matter currents and their role in energy extraction.

Findings

Magnetosphere satisfies the Znajek regularity condition

Energy is extracted primarily through matter currents

Geodesic congruences correspond to charged particles carrying energy and angular momentum

Abstract

The structural properties of geodesic currents in an ambient Kerr background is studied from an analytical point of view. The geodesics in the congruence correspond to charged particles that carry energy and angular momentum from the black hole through the Blandford-Znajek mechanism. It is shown that the resulting magnetosphere naturally satisfies the Znajek regularity condition. Particular attention is paid here to the energy extracted by matter currents rather than by electromagnetic Poynting fluxes.