Accelerating Bertotti-Robinson Black Holes in a Uniform Magnetic Field

TL;DR

This paper investigates how a uniform magnetic field and acceleration influence the physical properties, stability, and observable signatures of the accelerating Bertotti-Robinson black hole spacetime, including particle orbits, photon spheres, and emission rates.

Contribution

It provides detailed analytical and numerical analysis of particle dynamics, photon orbits, and emission characteristics in the deformed black hole spacetime with magnetic field and acceleration.

Findings

Magnetic field and acceleration shift the ISCO and photon sphere radii.

The stability of orbits is significantly affected by the magnetic field and acceleration.

The energy emission rate varies with magnetic field strength and acceleration parameter.

Abstract

We study the Hawking temperature, geodesic motion, and observable signatures of the accelerating Bertotti-Robinson (BR) spacetime, a vacuum black-hole solution deformed by a uniform magnetic field $B$ and an acceleration parameter $\alpha$. In the timelike sector, we derive the effective potential for massive particles, determine the specific energy and angular momentum for equatorial circular orbits, and determine how $(B,\alpha)$ shifts the ISCO; we also illustrate representative trajectories of massive particles. We then compute the radial and latitudinal epicyclic frequencies for small perturbations about circular orbits, quantifying how the magnetic field and acceleration modify local radial and vertical stability. In the null sector, we derive the photon effective potential and obtain analytical expressions for the photon-sphere radius, critical impact parameter, and shadow radius, complemented by photon trajectories, the effective radial force, and the Lyapunov exponent controlling the instability of circular null orbits; we also provide parameter-space maps for the photon sphere and shadow. Finally, we obtain the energy emission rate emitted from the black hole, showing how the acceleration parameter and the magnetic field affect this.