Photon capture cones and embedding diagrams of the Ernst spacetime

TL;DR

This paper compares photon capture cones and embedding diagrams of Schwarzschild and Ernst spacetimes, revealing how the magnetic field influences their geometric and optical properties.

Contribution

It introduces a detailed comparison of photon capture cones and embedding diagrams for Ernst spacetime, highlighting the effects of magnetic fields on spacetime geometry.

Findings

Photon escape cones are purely outward in Ernst spacetime.

Embedding diagrams shrink to zero radius asymptotically.

Regions with similar properties may exist in low magnetic field Ernst spacetimes.

Abstract

The differences between the character of the Schwarzschild and Ernst spacetimes are illustrated by comparing the photon capture cones, and the embedding diagrams of the $t=\mathrm{const}$ sections of the equatorial planes of both the ordinary and optical reference geometry of these spacetimes. The non-flat asymptotic character of the Ernst spacetime reflects itself in two manifest facts: the escape photon cones correspond to purely outward radial direction, and the embedding diagrams of both the ordinary and optical geometry shrink to zero radius asymptotically. Using the properties of the embedding diagrams, regions of these spacetimes which could have similar character are estimated, and it is argued that they can exist for the Ernst spacetimes with a sufficiently low strength of the magnetic field.