Affiliation: ZARM, University of Bremen, Germany

Title: Analytical studies of photon rings in black hole imaging

Abstract: Future observations are expected to reveal the so-called photon rings  in detailed images of black holes. These rings are lensed images of  luminous matter surrounding the black hole, formed by photons that  loop around it before reaching the observer. In this talk, we present  the results of analytical studies of photon rings in the images of  spherically symmetric black holes. Specifically, we derive an explicit  equation in polar coordinates that describes the shape of higher-order  photon rings. This formula characterizes the apparent shape of the  higher-order images of an equatorial emission ring of a given radius  around the black hole, as seen by a distant observer at an arbitrary  inclination. Additionally, we discuss how the black hole metric can be  constrained by measuring the relative separation between neighboring  photon rings, even without knowing the details of the emission.