Deflection of Light by a Rotating Black Hole Surrounded by "Quintessence"

TL;DR

This paper analyzes how a rotating black hole surrounded by quintessence, a dark energy-like fluid, affects light deflection, revealing that parameters like $w$ and $c$ influence the deflection angle, which can exceed Kerr spacetime predictions.

Contribution

It provides a detailed analysis of rotating black holes with quintessence, deriving conditions for their existence and quantifying how quintessence parameters affect light deflection.

Findings

Deflection angle depends on parameters $(c,w)$ with $cw<0$.

For $w oughly 0.1$ and $c<0$, deflection exceeds Kerr predictions.

An exact solution is derived for $w=-1/3$.

Abstract

We present a detailed analysis of a rotating black hole surrounded by "quintessence". This solution represents a fluid with a constant equation of state, $w$, which can for example describe an effective warm dark matter fluid around a black hole. We clarify the conditions for the existence of such a solution and study its structure by analyzing the existence of horizons as well as the extremal case. We show that the deflection angle produced by the black hole depends on the parameters $(c,w)$ which need to obey the condition $cw<0$ because of the weak energy condition, where $c$ is an additional parameter describing the hair of the black hole. In this context, we found that for $w\simeq 0.1$ (consistent with warm dark matter) and $c<0$, the deviation angle is larger than that in the Kerr spacetime for direct and retrograde orbits. We also derive an exact solution in the case of $w=-1/3$.