A gauge theoretical view of the charge concept inEinstein gravity

We will discuss some analogies between internal gauge theories and gravity in order to better understand the charge concept in gravity. A dimensional analysis of gauge theories in general and a strict deenition of elementary, monopole, and topological charges are applied to electromagnetism and to teleparallelism, a gauge theoretical formulation of Einstein gravity. As a result we inevitably nd that the gravitational coupling constant has dimension ~=l 2 , the mass parameter of a particle dimension ~=l, and the Schwarzschild mass parameter dimension l (where l means length). These dimensions connrm the meaning of mass as elementary and as monopole charge of the translation group, respectively. In detail, we nd that the Schwarzschild mass parameter is a quasi-electric monopole charge of the time translation whereas the NUT parameter is a quasi-magnetic monopole charge of the time translation as well as a topological charge. The Kerr parameter and the electric and magnetic charges are interpreted similarly. We conclude that each elementary charge of a Casimir operator of the gauge group is the source of a (quasi-electric) monopole charge of the respective Killing vector.