Testing Einstein Maxwell Power-Yang-Mills Hair via Black Hole Photon Rings

TL;DR

This study investigates how the hairy parameter in Einstein-Maxwell power-Yang-Mills black holes affects their photon rings and shadows, providing potential observational signatures to verify Yang-Mills hair.

Contribution

It introduces a detailed analysis of photon rings and shadows in Einstein-Maxwell power-Yang-Mills black holes, highlighting the impact of the hairy parameter on observable features.

Findings

Increasing hairy parameter decreases black hole shadow and photon ring size.

No degeneracy exists between photon ring and shadow in these black holes.

Photon ring and shadow can distinguish different black hole solutions.

Abstract

In this paper, the optical appearance of static and spherically symmetric hairy black holes is studied under the standard Einstein-Maxwell theory considering the p-power Yang-Mills term. During the research process, the specific case of $p=1/2$ was mainly selected for discussion. To understand the impact of the hairy parameter on black holes, we have studied the event horizon radius $r_{h} $, the photon sphere radius $r_{ph}$ and the radius of the innermost stable circular orbit $r_{isco}$ of this hairy black hole. Then, we utilized the backward ray-tracing method to analyze the geodesics of photons around this black hole and discussed the influence of the hairy parameter on the photon geodesics. In addition, we also calculated the unique shadow and photon ring of the black hole irradiated by a static thin accretion disk with three toy model emission functions. The research results show that as the hairy parameter gradually increases, the event horizon radius $r_{h} $, the photon sphere radius $r_{ph}$, the radius of the innermost stable circular orbit $r_{isco}$ and the critical impact parameter $b_{ph}$ of the black hole all exhibit a decreasing trend. Meanwhile, it also causes the area of the black hole shadow and the photon ring to decrease accordingly. Consequently, in the case of the static and spherically symmetric standard Einstein Maxwell power-Yang-Mills hairy black hole, there is no degeneracy in the photon ring and the shadow. Theoretically, it can reflect different black hole solutions and thus verify the Yang-Mills hair.