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

TL;DR

This work studies Kerr-Bertotti-Robinson black holes with a uniform magnetic field $B$, deriving their exact metric and horizon structure, and exploiting Hamilton–Jacobi separability to compute null geodesics. It analyzes how $B$ and spin $a$ shape photon regions and shadows, defines robust shadow observables, and develops a Kumar–Ghosh parameter-estimation framework to infer $(a,B)$ from shadow measurements while accounting for finite observer distance. The results show that $B$ enlarges and distorts shadows, reduces horizon-entropy via the conformal factor, and lowers Hawking temperature, leading to suppressed high-frequency energy emission, providing a potential observational avenue to probe horizon-scale magnetic fields with EHT/ngEHT. The methodology offers a concrete pathway to test non-Kerr spacetimes in strong gravity and to constrain magnetic backreaction effects in supermassive black holes using horizon-scale observations.

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 $θ$. 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.

Figures (8)

• Figure 1: Parameter space in the $(a, B)$ plane for KBRBHs. The shaded (blue) region corresponds to the existence of both inner and outer horizons. The boundary curve (red) represents the extremal black hole limit, beyond which no real horizons exist, even though it comes to a naked singularity or no-horizon spacetime. Increasing magnetic field strength $B$ restricts the allowed values of the spin parameter $a$, thus tightening the conditions for black hole formation.
• Figure 2: Comparison of the horizon structure between the KBRBHs and the Kerr black hole ($B = 0$) . The presence of a uniform magnetic field modifies the locations of the inner ($r_-$) and outer ($r_+$) horizons. As $B$ increases, the event horizons ($r_+$) shift outward.
• Figure 3: Cross-section of the event horizon ( red curve), stationary limit surface (SLS; blue curve), and ergoregion for KBRBHs with different magnetic field strengths $B$. Horizons get disconnected as the spin parameter $a$ or $B$ increases. Horizontal deformation is caused by increased magnetic fields. The ergoregion extends with both $a$ and $B$, while the SLS moves outward, indicating frame-dragging.
• Figure 4: Variation of the effective potential $V_{eff}$ for KBRBHs as a function of radial coordinate r with varying angular momentum $L_Z$ at $a/m=0.9$ (left) and $a/m=0.95$ (right) .
• Figure 5: Black hole shadow silhouettes of the KBRBH with various values of magnetic deviation parameter $B$ at $\theta_o=90^\circ$ , as shown for spin parameters $a/m = 0.9$ (left) and $a/m = 0.95$(right). As $B$ increases, the shadow size also increases and deviates from the Kerr case, revealing the effect of the external magnetic field on photon paths. The innermost contour represents the Kerr black hole.