Scattering at the angles of polyhedral rooms: Application to stress-energy tensor conservation in Riemannian spaces

Riemannian spaces with negative curvature constitute the proper setting for the distribution of images created by irregular polyhedral rooms with obtuse angles. The crucial parameter is the excess angle that arises around specific edges, called hinges, when first and second order images are considered, as it pilots the metric tensor of the space and all its geometrical properties. With the use of these geometrical properties, and complementing them with the uncertainty principle, we describe the scattering of wave packets around dihedral angles: it is proportional to the excess angle, and is best described in terms of the conservation of the stress-energy tensor. The basic elements for computing the scattering are given.