Black hole in a generalized Chaplygin-Jacobi dark fluid: shadow and light deflection angle

TL;DR

This paper models a black hole within a generalized Chaplygin-Jacobi dark fluid, deriving its metric, analyzing light deflection and shadow, and constraining model parameters using Event Horizon Telescope data.

Contribution

It introduces a new black hole solution in a dark fluid with anisotropic properties and analyzes its observable effects, such as shadow and light deflection, with parameter constraints.

Findings

Parameter constraints: 0 ≤ B < 0.03, 0 < α < 0.1

Estimated Einstein ring radius: approximately 37.6 microarcseconds

Derived analytical and approximate solutions for spacetime and light behavior

Abstract

We investigate a generalized Chaplygin-like gas with an anisotropic equation of state, characterizing a dark fluid within which a static spherically symmetric black hole is assumed. By solving the Einstein equations for this black hole spacetime, we explicitly derive the metric function. The spacetime is parametrized by two critical parameters, $\mathcal{B}$ and $\alpha$, which measure the deviation from the Schwarzschild black hole and the extent of the dark fluid's anisotropy, respectively. We explore the behavior of light rays in the vicinity of the black hole by calculating its shadow and comparing our results with the Event Horizon Telescope observations. This comparison constrains the parameters to $0 \leq \mathcal{B} < 0.03$ and $0 < \alpha < 0.1$. Additionally, we calculate the deflection angles to determine the extent to which light is bent by the black hole. These calculations are further utilized to formulate possible Einstein rings, estimating the angular radius of the rings to be approximately $37.6\,\mathrm{\mu as}$. Throughout this work, we present analytical solutions wherever feasible, and employ reliable approximations where necessary to provide comprehensive insights into the spacetime characteristics and their observable effects.