Optical appearance of Einstein-Æther black hole surrounded by thin disk

In Einstein-Æther theory, the Lorentz symmetry is locally broken in the high-energy regime due to the presence of the Æther field. This shall leave significant imprint on astronomical observation. In this paper, we investigate the optical appearance of two types of the static and spherically symmetric black holes in Einstein-Æther theory. Via Euler-Lagrange equation, we obtain the equations of motion of the photon and calculate the total deflection angle of the photon trajectory around the black hole. By classifying the light rays with the total number of orbits, we study the effects of coupling constants on the direct image, lensing ring, and photon ring. The features of the light trajectories are also investigated by comparing with the Einstein-Æther theory and general relativity. Moreover, we also show the explicit optical appearance of black holes surrounded by thin disk emissions with three characteristic emitted models. The results indicate that the direct image gives the main contribution to the total flux, and the lensing ring just gives a very small contribution, whereas the role of the photon ring is negligible. The optical appearances are also found to significantly rely on these coupling constants.