Spherical photon orbits around a rotating black hole with quintessence and cloud of strings

TL;DR

This paper provides an analytical study of spherical photon orbits around a rotating black hole influenced by quintessence and a cloud of strings, including orbit radii, impact parameters, and stability conditions.

Contribution

It offers the first full analytical solutions for photon orbits in this complex black hole spacetime, including equatorial and inclined orbits using elliptic functions.

Findings

Analytical expressions for radii of spherical photon orbits

Derivation of impact parameter profiles and extreme cases

Conditions for orbit stability and period calculations

Abstract

In this paper, we calculate the analytical solutions for the radii of planar and polar spherical photon orbits around a rotating black hole that is associated with quintessential field and cloud of strings. This includes a full analytical treatment of a quintic that describes orbits on the equatorial plane. Furthermore, The radial profile of the impact parameters is studied and the radii corresponding to the extreme cases are derived. For the more general cases, we also discuss the photon regions that form around this black hole. To simulate the orbits that appear in different inclinations, we analytically solve the latitudinal and azimuth equations of motion in terms of the Weierstrassian elliptic functions, by considering the radii of spherical orbits, in their general form, as the initial conditions. The period and the stability conditions of the orbits are also obtained analytically.