Black hole photon ring beyond General Relativity: an integrable parametrization
This paper introduces a symmetry-preserving "Kerr off-shell" parametrization to analytically derive the photon ring's critical curve in beyond-Kerr geometries, demonstrating that the circlipse fitting function suffers from significant degeneracy where identical ring shapes can arise from distinct combinations of mass, spin, and deviation parameters, thereby necessitating independent measurements of mass and spin to rigorously test the Kerr hypothesis.