Analysis of regular black hole with multi-polytropic equation of state under various backgrounds

Abstract

The purpose of this work is to examine the weak deflection angle, shadow, Regge–Wheeler potential, and greybody factor of a black hole with a multi-polytropic equation of state. In the weak field limit, we use the Gauss–Bonnet theorem along with the Gibbons and Werner method to find the photon’s ray’s deflection angle. Furthermore, we demonstrate how plasma and non-plasma mediums behave with respect to the deflection of photons. Similarly, we examine the graphical effects of the deflection angle on a black hole with a multi-polytropic equation of state, by considering both plasma and non-plasma medium. We also investigate the shadow of a black hole using a multi-polytropic equation of state. Furthermore, we improve our interest by including the spin-dependent Regge–Wheeler potential, which determines the dynamics of perturbations in the presence of the polytropic equation of state black hole. Our analysis of the Regge–Wheeler potential for different spin fields reveals the impact of parameters on its form when monopoles are present. Our study also focused on the rigorous bounds of the black hole with respect to the greybody factor, as well as its graphical behaviour.