Magnetized discs and photon rings around Yukawa-like black holes

TL;DR

This paper models magnetized thick discs around non-rotating black holes within an $f(R)$-gravity framework, analyzing how Yukawa-like modifications influence disc properties and photon ring sizes, with implications for observational constraints.

Contribution

It introduces analytical solutions for magnetized tori in $f(R)$-gravity, exploring deviations from general relativity and their effects on disc and photon ring characteristics.

Findings

Small $\delta$ deviations cause minor horizon and disc edge shifts.

Larger $\delta$ values significantly alter black hole and disc properties.

Photon ring size constraints help limit $f(R)$-gravity parameters.

Abstract

We present stationary solutions of geometrically thick discs (or tori) endowed with a self-consistent toroidal magnetic field distribution surrounding a non-rotating black hole in an analytical, static, spherically-symmetric $f(R)$-gravity background. These $f(R)$-gravity models introduce a Yukawa-like modification to the Newtonian potential, encoded in a single parameter $\delta$ which controls the strength of the modified potential and whose specific values affect the disc configurations when compared to the general relativistic case. Our models span different magnetic field strengths, from purely hydrodynamical discs to highly magnetized tori. The characteristics of the solutions are identified by analyzing the central density, mass, geometrical size, angular size, and the black hole metric deviations from the Schwarzschild space-time. In the general relativistic limit ($\delta=0$) our models reproduce previous results for a Schwarzschild black hole. For small values of the $\delta$ parameter, corresponding to $\sim 10\%$ deviations from general relativity, we find variations of $\sim 2 \%$ in the event horizon size, a $\sim 5\%$ shift in the location of the inner edge and center of the disc, while the outer edge increases by $\sim 10\%$. Our analysis for $|\delta|>0.1$, however, reveals notable changes in the black hole space-time solution which have a major impact in the morphological and thermodynamical properties of the discs. The comparison with general relativity is further investigated by computing the size of the photon ring produced by a source located at infinity. This allows us to place constraints on the parameters of the $f(R)$-gravity model based on the Event Horizon Telescope observations of the size of the light ring in M87 and SgrA$^*$.