Disc sources for Conformastationary metrics

TL;DR

This paper investigates conformastationary metrics in Einstein-Maxwell theory, revealing that such metrics require hoop tensions alongside moving charged dust as sources, and provides explicit examples with disk sources.

Contribution

It demonstrates that conformastationary metrics necessitate hoop tensions in addition to moving dust, and constructs explicit disk source solutions, extending understanding of their source structure.

Findings

Hoop tensions are essential for axially symmetric conformastationary metrics.

Explicit solutions with disk sources are derived.

Generalizations to non-axially symmetric cases are discussed.

Abstract

Conformastationary metrics have been derived by Perjes and by Israel and Wilson as source-free solutions of the Einstein-Maxwell equations. By analogy with the conformastatic metrics which have charged dust sources it was assumed that conformastationary metrics would be the external metrics of charged dust in steady motion. However for axially symmetric conformastationary metrics we show that, as well as moving dust, hoop tensions are always necessary to balance the centrifugal forces induced by the motion. Exact examples of conformastationary metrics with disk sources are worked out in full. Generalisations to non-axially symmetric conformastationary metrics are indicated.