Photon spheres and spherical accretion image of a hairy black hole

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.