Abstract
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 definition 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 find that the gravitational coupling constant has dimension ℏ/l 2, the mass parameter of a particle dimension ℏ/l, and the Schwarzschild mass parameter dimension l (where l means length). These dimensions confirm the meaning of mass as elementary and as monopole charge of the translation group, respectively. In detail, we find 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.
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Toussaint, M. A Gauge Theoretical View of the Charge Concept in Einstein Gravity. General Relativity and Gravitation 32, 885–896 (2000). https://doi.org/10.1023/A:1001985024409
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DOI: https://doi.org/10.1023/A:1001985024409