Geodesics and Shadows in the Kerr-Bertotti-Robinson Black Hole Spacetime

TL;DR

This paper analyzes null and timelike geodesics in the Kerr-Bertotti-Robinson spacetime, deriving analytical expressions for photon spheres and black hole shadows, and examining how magnetic fields influence observable shadow features.

Contribution

It provides the first analytical treatment of null geodesics and shadows in the Kerr-Bertotti-Robinson spacetime, including perturbative expressions for photon spheres and shadow deviations due to magnetic fields.

Findings

Null geodesics are separable and analytically solvable.

Photon sphere and ISCO expressions are derived perturbatively.

Magnetic fields cause measurable deviations in black hole shadows.

Abstract

In this work, we investigate geodesics and black hole shadows in the Kerr-Bertotti-Robinson spacetime. We show that the equations of motion for null geodesics are separable and admit analytical treatment, whereas timelike geodesics are generally non-separable. Approximate analytical expressions for the photon sphere and the innermost stable circular orbit are derived via perturbative expansions in the magnetic field strength. We further explore the black hole shadow using both numerical and analytical methods, examining the effects of the magnetic field, the observer's inclination angle and radial position. Deviations from the standard Kerr shadow are quantified, and a physical interpretation is provided by introducing asymptotic regimes defined relative to the magnetic field strength.