A geometric approach for radiation transport inside complex systems

The aim of this Letter is to extend the phenomenological theory of radiation transfer to complex systems. For elastic or electromagnetic waves, one presents a geometrization of matter based on relativistic gravitation models. In this approach, particles experience material media as curved spacetimes, which locally affect the energetic processes. The general form of Clausius invariant is calculated and the curved radiative transfer equation is derived. An application to phonon transport in solids shows that the presence of a defect can amplify the elastic energy carried in particular directions of propagation.