Parameter estimation of Kerr-Bertotti-Robinson black holes using their shadows

TL;DR

This paper studies how magnetic fields affect the shadows of Kerr-Bertotti-Robinson black holes, revealing that magnetic strength influences shadow size, shape, and Hawking radiation, aiding in distinguishing these from Kerr black holes.

Contribution

It provides a detailed analysis of black hole shadows in magnetic field-influenced spacetimes, introducing new parameter estimation methods and exploring observational signatures.

Findings

Increasing magnetic field B enlarges the shadow and causes distortions.

Shadow observables like area and oblateness depend on spin and magnetic parameters.

Magnetic fields suppress Hawking radiation, lowering the temperature.

Abstract

We investigate the shadow of Kerr-Bertotti-Robinson black holes (KBRBHs), which have a deviation parameter $B$ that captures the effect of an external magnetic field on the spacetime geometry. These spacetimes of Petrov type $D$ are asymptotically non-flat. We utilise the separability of the Hamilton-Jacobi equation to generate null geodesics and examine the crucial impact parameters for unstable photon orbits that define the black hole shadow. We carefully investigate how the magnetic field strength $B$ and spin parameter $a$ influence black hole shadows, discovering that increasing $B$ increases the shadow size while also introducing additional distortions, especially at high spins. We calculate the shadow observables, viz., area $A$ and oblateness $D$ and create contour plots in the parameter space $(a, B)$ to facilitate parameter estimation. We also investigate the dependence of the shadow on the observer's position, specifically by altering the radial coordinate $r_O$ and the inclination angle $\theta$. For far viewers, the shadow approaches its asymptotic shape, but finite-distance observers perceive substantial deviations. The energy emission rate analysis reveals that the magnetic field parameter $B$ modifies the Hawking radiation spectrum, with increasing $B$ suppressing emission via backreaction, which lowers the Hawking temperature. Our findings confirm that KBRBH shadows encode imprints of magnetic deviations, thereby offering a potential avenue to distinguish Kerr from non-Kerr spacetimes and to probe magnetic effects in the strong-gravity regime.