English

Melvin-Zipoy-Voorhees Spacetime and Circular Orbits

General Relativity and Quantum Cosmology 2026-01-30 v1

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 kk. 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 bb 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.

Keywords

Cite

@article{arxiv.2601.21793,
  title  = {Melvin-Zipoy-Voorhees Spacetime and Circular Orbits},
  author = {Haryanto M. Siahaan},
  journal= {arXiv preprint arXiv:2601.21793},
  year   = {2026}
}

Comments

19 pages, 6 figures

R2 v1 2026-07-01T09:25:49.747Z