Melvin-Zipoy-Voorhees Spacetime and Circular Orbits

TL;DR

This paper introduces an exact magnetized extension of the Zipoy-Voorhees spacetime, analyzing how magnetic fields influence the structure and circular orbits of particles and photons.

Contribution

It constructs a new magnetized spacetime solution using the Harrison transformation and studies its effects on particle dynamics and spacetime algebraic properties.

Findings

Magnetic field causes inward shift of ISCO.

Photon ring radius slightly increases with magnetization.

Spacetime is generally Petrov type I.

Abstract

We construct an exact magnetized generalization of the Zipoy-Voorhees spacetime by applying the magnetic Harrison transformation to a static seed with quadrupolar deformation parameter $k$. The resulting Melvin-Zipoy-Voorhees metric is a solution to the Einstein-Maxwell equations that interpolates between the unmagnetized Zipoy-Voorhees geometry and the Melvin magnetic universe. We analyze the algebraic structure, finding the spacetime to be generically of Petrov type I, and investigate the equatorial dynamics of charged test particles and photons. Our analysis reveals that the external magnetic field $b$ induces a ``Lorentz shift'' in the effective angular momentum, suppressing the potential barrier and causing the Innermost Stable Circular Orbit (ISCO) to migrate inward. In contrast, the radius of the photon ring shifts slightly outward with increasing magnetization.