The effect of scalar hair on the charged black hole with the images from accretions disk

TL;DR

This study explores how scalar hair affects the optical properties of charged black holes, revealing observable differences in accretion disk images that could distinguish them from standard Reissner-Nordström black holes.

Contribution

It introduces a detailed analysis of scalar hair effects on black hole optical features, highlighting potential observational signatures in accretion disk images.

Findings

Differences in effective potentials, photon sphere radii, and ISCO between CSH and RN black holes.

No significant difference in the critical impact parameter $b_{ph}$.

Charge parameter $Q$ significantly influences brightness distributions in accretion disk images.

Abstract

In this paper, we investigate the optical properties of a charged black hole with scalar hair (CSH) within the context of four-dimensional Einstein-Maxwell-Dilaton gravity. To achieve this, we consider three distinct toy models of thin accretion disks. The presence of dilaton coupling allows us to express both the solutions of CSH and the Reissner-Nordstr\"om (RN) black hole in terms of their mass ($M$) and charge ($Q$). Our findings reveal differences in the effective potentials $V_{eff}$, photon sphere radii $r_{ph}$, and innermost stable circular orbit $r_{isco}$ between the CSH and RN black hole cases, which become increasingly pronounced as the charge parameter $Q$ increases. However, no noticeable distinctions are observed concerning the critical impact parameter $b_{ph}$. When the ratio of the photon ring band and the lensed ring band exceeds 0.1, it may suggest the presence of a charged black hole with scalar hair. Furthermore, our results underscore the significant influence of the charge parameter $Q$ on the brightness distributions of the direct, lensed ring, and photon ring for three standard emission functions. These findings emphasize the potential for distinguishing between CSH and RN black holes through an analysis of direct intensity and peak brightness in specific accretion disk models.