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A gauge theoretical view of the charge concept in Einstein gravity | | Marc Toussaint
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6 Jul 1999 | | Journal: | Gen.Rel.Grav. 32 (2000) 885-896 | | Subject: | gr-qc hep-th | | 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 $hbar/l^2$, the mass parameter of a particle dimension $hbar/l$, 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. | | Source: | arXiv, gr-qc/9907024 | | Services: | Forum | Review | PDF | Favorites | |
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