Photon Rings around Kerr and Kerr-like Black Holes

TL;DR

This paper develops semi-analytic models of photon ring shapes around Kerr and Kerr-like black holes, providing a potential observational test for deviations from the Kerr metric and the no-hair theorem.

Contribution

It introduces new semi-analytic expressions for photon ring shapes around Kerr-like black holes, enabling detection of deviations from Kerr geometry.

Findings

Photon rings are affected by deviations causing asymmetry.

Ring asymmetry can indicate violation of the no-hair theorem.

Approximate formulas for ring diameter, displacement, and asymmetry are provided.

Abstract

Very-long baseline interferometric observations have resolved structure on scales of only a few Schwarzschild radii around the supermassive black holes at the centers of our Galaxy and M87. In the near future, such observations are expected to image the shadows of these black holes together with a bright and narrow ring surrounding their shadows. For a Kerr black hole, the shape of this photon ring is nearly circular unless the black hole spins very rapidly. Whether or not, however, astrophysical black holes are truly described by the Kerr metric as encapsulated in the no-hair theorem still remains an untested assumption. For black holes that differ from Kerr black holes, photon rings have been shown numerically to be asymmetric for small to intermediate spins. In this paper, I calculate semi-analytic expressions of the shapes of photon rings around black holes described by a new Kerr-like metric which is valid for all spins. I show that photon rings in this spacetime are affected by two types of deviations from the Kerr metric which can cause the ring shape to be highly asymmetric. I argue that the ring asymmetry is a direct measure of a potential violation of the no-hair theorem and that both types of deviations can be detected independently if the mass and distance of the black hole are known. In addition, I obtain approximate expressions of the diameters, displacements, and asymmetries of photon rings around Kerr and Kerr-like black holes.