Magnetic Modification of Black Hole Photospheres with Image Contraction, Efficiency Shifts and Redshift Boosts in Schwarzschild-Bertotti-Robinson Spacetime

TL;DR

This paper explores how a uniform magnetic field influences the optical and radiative properties of accretion disks around Schwarzschild black holes within the Schwarzschild-Bertotti-Robinson spacetime, revealing significant modifications in photon trajectories, characteristic radii, and radiative efficiency.

Contribution

It introduces a detailed analysis of magnetic field effects on black hole accretion disks, including shifts in key radii and the development of an analytical framework for disk dynamics in this spacetime.

Findings

Magnetic fields cause the photon sphere, event horizon, and ISCO to increase in radius.

Accretion disk images contract and radiative fluxes are enhanced with magnetic field strength.

Radiative efficiency decreases by approximately 91% at moderate magnetic field strengths.

Abstract

We investigate the optical and radiative signatures of an accretion disk around a Schwarzschild black hole (BH) immersed in a uniform magnetic field. The spacetime geometry is described by the Schwarzschild-Bertotti-Robinson (SBR) metric, which represents the non-rotating sector of the recently discovered Kerr-Bertotti-Robinson exact solution to the Einstein-Maxwell equations. We begin with the study of null geodesics and demonstrate that the self-consistent magnetic field fundamentally alters photon propagation, causing an expansion of light bundles relative to the Schwarzschild case due to modified initial conditions in the orbital equation. We then compute the magnetic field-dependent shifts of key characteristic radii: the event horizon ($r_h$), photon sphere ($r_{ph}$), and innermost stable circular orbit ($r_{ISCO}$). We find that all three increase monotonically with field strength $B$, revealing a magnetic amplification of the effective gravitational field. For $B=0.05$, we find that the lensed emission bands contract to a narrower impact parameter range, $b\in(4.976,5.149)\cup(5.19,6.128)$. Employing ray-tracing formalism, we construct observed accretion disk images and quantify magnetic modifications, showing that the direct image contracts while maximum energy flux, radiation temperature, and redshift factor are enhanced. Complementing these numerical findings, we develop an analytical framework for the accretion disk dynamics. We derive the modified Keplerian frequency $\Omega_K$, along with the specific energy $E$ and angular momentum $L$ for circular orbits. From these, we obtain the exact ISCO radius $r_{\text{ISCO}}$, which shows an outward shift. This outward shift reveals that the radiative efficiency decreases dramatically with increasing magnetic field strength $B$. For $\beta = BM \sim 0.1$, the efficiency drops by approximately $91\%$.