Frame dragging, vorticity and electromagnetic fields in axially symmetric stationary spacetimes

TL;DR

This paper explores how electromagnetic fields influence frame dragging and vorticity in axially symmetric stationary spacetimes, providing new formulas and analyzing specific cases like rotating charged magnetic dipoles.

Contribution

It derives general relations between vorticity and electromagnetic Poynting vector, linking electromagnetic energy flow to inertial frame dragging in stationary spacetimes.

Findings

Poynting vector plays a key role in frame dragging effects.

In vacuum, static spacetimes have zero magnetic part of Weyl tensor.

Detailed analysis of rotating massive charged magnetic dipole.

Abstract

We present a general study about the relation between the vorticity tensor and the Poynting vector of the electromagnetic field for axially symmetric stationary electrovacuum metrics. The obtained expressions allow to understand the role of the Poynting vector in the dragging of inertial frames. The particular case of the rotating massive charged magnetic dipole is analyzed in detail. In addition, the electric and magnetic parts of the Weyl tensor are calculated and the link between the later and the vorticity is established. Then we show that, in the vacuum case, the necessary and sufficient condition for the vanishing of the magnetic part is that the spacetime be static.