Observational signatures of a static $f(R)$ black hole with thin accretion disk

Abstract

In this study, we focus on a static spherically symmetric $f(R)$ black hole spacetime characterized by a linear dark matter-related parameter. Our investigation delves into understanding the influence of different assumed values of this parameter on the observable characteristics of the black hole. To fulfill this task, we investigate the light deflection angles, which are inferred from direct analytical calculations of null geodesics.} To examine the black hole's properties further, we assume an optically thin accretion disk and explore various emission profiles. Additionally, we investigate the shadow cast by the illuminated black hole when affected by the disk. Furthermore, we simulate the brightness of an infalling spherical accretion in the context of silhouette imaging for the black hole. Our findings indicate that, except for some specific cases, the observed brightness of the accretion disk predominantly arises from direct emission, rather than lensing and photon rings. Moreover, we reveal that the linear dark parameter of the black hole significantly influences the shadow size and brightness. Our discussion covers both analytical and numerical approaches, and we utilize ray-tracing methods to produce accurate visualizations.

28 pages, 87 figures

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• Shadows, rings and optical appearance of a magnetically charged regular black hole illuminated by various accretion disks
• Null geodesics, causal structure, and matter accretion in Lorentzian-Euclidean black holes
• Signatures of the accelerating black holes with a cosmological constant from the ${\text{Sgr A}}^{\star }$ and ${\text{M87}}^{\star }$ shadow prospects
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• Shadows and Observational Images of a Schwarzschild-like Black Hole Surrounded by a Dehnen-type Dark Matter Halo
• Accretion of matter of a new bumblebee black hole