Shadows of black hole surrounded by anisotropic fluid in Rastall theory

TL;DR

This paper investigates the shadow of rotating black holes surrounded by anisotropic fluid in Rastall gravity, deriving an analytical formula and visualizing how parameters affect the shadow shape, providing a way to test alternative gravity theories.

Contribution

It introduces a new model of rotating Rastall black holes with anisotropic fluid, deriving an analytical shadow formula, and explores parameter effects on black hole shadows for observational tests.

Findings

Derived an analytical formula for the shadow of rotating Rastall black holes.

Visualized shadow variations with different parameters and observer positions.

Identified additional horizons in Rastall black holes affecting shadow structure.

Abstract

Due to the gravitational lensing effect, a black hole casts a shadow larger than its horizon over a bright background, and the shape and size can be calculated. The Event Horizon Telescope collaboration has produced the first direct image (shadow) of the black hole and it is in accordance with the shadow of a Kerr black hole of general relativity. However, deviations from the Kerr black hole arising from modified theories of gravity are not ruled out and they are important as they offer an arena to test these theories through astrophysical observation. This stimulates us to investigate rotating black holes surrounded by anisotropic fluid in Rastall theory namely a rotating Rastall black hole, which is characterized by mass $M$, spin $a$, field structure parameter $N_s$ and the Rastall parameter $\psi$. It encompasses, as special cases, Kerr ($N_s \to 0$) and Kerr-Newman ($s=0$ and $N_s = -Q^2 $) black holes. The rotating Rastall black hole is characterized by an additional cosmological-like horizon apart from Cauchy and event horizons. We derive an analytical formula for the shadow of a rotating Rastall black hole and go on to visualize the shadow of black holes for various values of the parameters for an observer at a given coordinate ($r_O, \theta_O$) in the domain $[r_+,r_q]$.