Shadows and Optical Appearances of Black Holes in $R^{2}$ Gravity

TL;DR

This paper investigates the optical properties and shadows of charged and rotating black holes in $R^{2}$ gravity, comparing theoretical predictions with observational data from M87$^{\star}$ to constrain model parameters.

Contribution

It introduces a rotating black hole solution in $R^{2}$ gravity using the Newman-Janis algorithm and analyzes its optical features and energy emission rates.

Findings

Black hole shadows in $R^{2}$ gravity are characterized and compared with observational data.

Rotation and parameters significantly influence the energy emission rate and shadow size.

Constraints on $R^{2}$ gravity parameters are derived from M87$^{\star}$ observations.

Abstract

In this paper, we consider a charged AdS/dS black hole (BH) in $R^{2}$ gravity and study its optical features, including the shadow's geometrical shape and the energy emission rate. Additionally, we look for criteria to restrict the free parameters of the theory by comparing them to observational data of M87$^{\star}$. Then, we employ the Newman-Janis algorithm to build the rotating counterpart of the static solution in $R^{2}$ gravity and calculate the energy emission rate for the rotating case as well as discuss how the rotation factor and other parameters of this theory affect the emission of particles around the BHs. In the following, we consider the obtained rotating BH as a supermassive black hole and evaluate the parameters of the model with shadow size estimates based on the observations of M87$^{\star}$ from EHT.