Gravitational field and lensing of a circular chiral vorton

Abstract

We derive the metric of a circular chiral vorton in the weak field limit. The object is self-supporting by means of its chiral current. A conical singularity with deficit angle, identical to that of straight string with the same linear mass density, is present at the vorton's core. We find that the metric is akin to the electromagnetic $4$-potential of a circular current wire loop, illustrating the concept of gravito-electromagnetism. Surprisingly we find that the solution asymptotically mimics a Kerr-like naked singularity with mass $M_v=4\pi R\mu$ and spin parameter $a=R/2$. Finally, we also simulate the gravitational lensing images by solving the corresponding null geodesic equations. This reveals interesting properties of the images, such as the simultaneous creation of a minimally distorted source image and its Einstein ring, as well as the formation of double images on the back side of the ring.