Abstract
The group velocity of light in material around the AGN jet is acquiescently one (c as a unit), but this is only a hypothesis. Here, we re-derive apparent superluminal and Doppler formulas for the general case (it is assumed that the group velocity of light in the uniform and isotropic medium around a jet (a beaming model) is not necessarily equal to one, e.g., Araudo et al. (2010) thought that there may be dense clouds around AGN jet base), and show that the group velocity of light close to one could seriously affect apparent superluminal phenomena and Doppler effect in the AGN jet (when the viewing angle and Lorentz factor take some appropriate values).
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