Point Charge Self-Energy in the General Relativity

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 $\text{d}$-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 $m{c}^2$, while for the Kerr and Kerr–Newman solutions the angular momentum is $mc\mathbf{a}$. 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.