Point Charge Self-Energy in the General Relativity

Details Point Charge Self-Energy in the General Relativity Point Charge Self-Energy in the General Relativity

2005-04-21

arxiv.org/abs/gr-qc/0504097v1

Int.J.Mod.Phys. A20 (2005) 2288-2294

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

VI Fridmann Seminar, France, Corsica, Corgeze, 2004, LaTeX, 6 pages, 2 figes

Scientific paper

10.1142/S0217751X05024511

Singularities in the metric of the classical solutions to the Einstein equations (Schwarzschild, Kerr, Reissner -- Nordstr\"om and Kerr -- Newman solutions) lead to appearance of generalized functions in the Einstein tensor that are not usually taken into consideration. The generalized functions can be of a more complex nature than the Dirac $\d$-function. To study them, a technique has been used based on a limiting solution sequence. The solutions are shown to satisfy the Einstein equations everywhere, if the energy-momentum tensor has a relevant singular addition of non-electromagnetic origin. When the addition is included, the total energy proves finite and equal to $mc^2$, while for the Kerr and Kerr--Newman solutions the angular momentum is $mc {\bf a}$. As the Reissner--Nordstr\"om and Kerr--Newman solutions correspond to the point charge in the classical electrodynamics, the result obtained allows us to view the point charge self-energy divergence problem in a new fashion.

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