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In this note we revisit the emergent conformal symmetry in the near-ring region of warped spacetime. In particular, we propose a novel construction of the emergent near-ring sl(2, ℝ)QNM symmetry. We show that each eikonal QNM family falls into one highest-weight representation of this algebra, and sl(2, ℝ)QNM can be related to the near-ring isometry group sl(2, ℝ)ISO in a simple way. Furthermore we find that the coherent state space of sl(2, ℝ)QNM can be identified with the phase space of the photon ring.

In this work, we derive two formulas encoding the polarization direction and luminosity of synchrotron radiations from the moving electrons in curved spacetime under the geometric optics approximation. As an application, we further study the polarized images of synchrotron radiations from electron sources in Schwarzschild black hole spacetime with a vertical and uniform magnetic field. In particular, by focusing on the circular orbits of electrons on the equatorial plane, we show the polarized images of the synchrotron radiations from these orbits for different observational angles and discuss the variations of the polarization directions concerning the angles.