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Distributional Sources for Newman's Holomorphic Field | | Gerald Kaiser
; | | Date: |
15 Aug 2001 | | Journal: | J.Phys. A37 (2004) 8735-8746 | | Subject: | General Relativity and Quantum Cosmology; Mathematical Physics | gr-qc math-ph math.MP | | Abstract: | In 1973, E. T. Newman considered the holomorphic extension ilde E(x+iy) of the Coulomb field E(x) in R^3. By analyzing its multipole expansion, he showed that the real and imaginary parts of ilde E(x+iy), viewed as functions of x for fixed y, are the electric and magnetic fields generated by a spinning ring of charge R. This represents the electromagnetic part of the Kerr-Newman solution to the Einstein-Maxwell equations. As already pointed out by Newman and Janis in 1965, this interpretation is somewhat problematic since the fields are double-valued. To make them single-valued, a branch cut must be introduced so that R is replaced by a charged disk D having R as its boundary. In the context of curved spacetime, D becomes a spinning disk of charge and mass representing the singularity of the Kerr-Newman solution. Here we confirm the above interpretation of the real and imaginary parts of ilde E(x+iy) by computing the charge- and current densities directly as distributions in R^3 supported in the source disk D. This shows in particular that D spins rigidly at the critical rate, so that its rim R moves at the speed of light. It is a pleasure to thank Ted Newman, Andrzej Trautman and Iwo Bialinicki-Birula for many instructive discussions, particularly in Warsaw and during a visit to Pittsburgh. | | Source: | arXiv, gr-qc/0108041 | | Services: | Forum | Review | PDF | Favorites | |
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