Photon Spheres and Spherical Accretion Image of a Hairy Black Hole

TL;DR

This paper investigates the photon spheres and accretion images of a class of hairy black holes, revealing the existence of one or two photon spheres and their optical signatures, including bright rings and shadows.

Contribution

It demonstrates the presence of two unstable photon spheres in hairy black holes and analyzes their impact on observable accretion images, including shadow boundaries.

Findings

Two unstable photon spheres exist for certain parameters.

Accretion images show one or two bright rings depending on photon sphere number.

Shadow radius varies with black hole charge, shrinking to zero at critical charge.

Abstract

In this paper, we first consider null geodesics of a class of charged, spherical and asymptotically flat hairy black holes in an Einstein-Maxwell-scalar theory with a non-minimal coupling for the scalar and electromagnetic fields. Remarkably, we show that there are two unstable circular orbits for a photon in a certain parameter regime, corresponding to two unstable photon spheres of different sizes outside the event horizon. To illustrate the optical appearance of photon spheres, we then consider a simple spherical model of optically thin accretion on the hairy black hole, and obtain the accretion image seen by a distant observer. In the single photon sphere case, only one bright ring appears in the image, and is identified as the edge of the black hole shadow. Whereas in the case with two photon spheres, there can be two concentric bright rings of different radii in the image, and the smaller one serves as the boundary of the shadow, whose radius goes to zero at the critical charge.