Kirchhoff Paradigm over Curved Manifolds

Pioneered by Alfred Fettweis, a methodology of mapping linear and nonlinear problems of physical origin to multidimensional continuous domain Kirchhoff circuits, that he called the Kirchhoff Paradigm, enjoyed remarkable success. While it is known that a large variety of physical problems including those described by the nonlinear fluid dynamical equations e.g., the Navier-Stokes equation yields to this analysis, an open-ended goal of this research program had been to demonstrate that most problems with origin in (classical) physics can be modeled in this way. In this paper, it is shown by assembling a number of already known results that the methodology, in fact, applies to problems defined over curvilinear manifolds as well. Following Alfred Fettweis' suggestions the paper thus presents an argument in favor of the potential of Kirchhoff paradigm for modeling problems in which relativistic considerations must be taken into account.