Derivation of the Radiative Transfer Equation Inside a Moving Semi-Transparent Medium of Non Unit Refractive Index

Abstract: The derivation of the radiative transfer equation inside a moving semi-transparent medium of non unit constant refractive index has been completely achieved, leading to an exactly similar equation as in the case of a unit index, unless it is expressed in a particular frame with particular time and space co-ordinates; defining first the “equivalent vacuum ” and the “matter” space associated to its “matter ” co-ordinates with the help of the Gordon’s metric, it is shown that an observer at rest in vacuum perceives the isotropic moving medium as an anisotropic uniaxial medium of given optical axis, for which it is possible to derive general transmission and reflection rules for electromagnetic fields; however the exhibited refractive index characterising the moving medium, relatively to the observer located in vacuum, is not an effective index but only an apparent one without any energetic significance, and the specific intensity must be obtained relatively to a given observer at rest located inside the moving medium; finally the general form of the radiative transfer equation is obtained in the moving medium