Department of Applied Mathematics, The Weizmann Institute, Rehovot, Israel.
Proc Natl Acad Sci U S A. 1982 Oct;79(20):6404-8. doi: 10.1073/pnas.79.20.6404.
Adopting, with Schwarzschild, the Einstein gauge ((munu) = -1), a solution of Einstein's field equations for a charged mass point of mass M and charge Q is derived, which differs from the Reissner-Nordstrøm solution only in that the variable r is replaced by R = (r(3) + a(3))((1/3)), where a is a constant. The Newtonian gravitational potential psi identical with (2/c(2))(1 - g(00)) obeys exactly the Poisson equation (in the R variable), with the mass density equal to (E(2)/4pic(2)), E denoting the electric field. psi also obeys a second linear equation in which the operator on psi is the square root of the Laplacian operator. The electrostatic potential Phi (= Q/R), psi, and all the components of the curvature tensor remain finite at the origin of coordinates. The electromagnetic energy of the point charge is finite and equal to (Q(2)/a). The charge Q defines a pivotal mass M() = (Q/G((1/2))). If M < M(*), then the whole mass is electromagnetic. If M > M(), the electromagnetic part of the mass M(em) equals [M - (M(2) - M(2))((1/2))], whereas the material part of the mass M(mat) equals (M(2) - M(2))((1/2)). When M > M(), the constant a is determined, following Schwarzschild, by shrinking the "Schwarzschild radius" to zero. When M < M(), a is determined so as to make the gravitational acceleration vanish at the origin.
采用 Schwarzschild 的 Einstein 规范（(munu) = -1），从 Einstein 场方程推导出一个带有质量 M 和电荷 Q 的点电荷的解，该解与 Reissner-Nordstrøm 解的不同之处仅在于变量 r 被 R = (r(3) + a(3))((1/3)) 所取代，其中 a 是一个常数。牛顿引力势 psi 与 (2/c(2))(1 - g(00)) 完全相同，它严格满足 Poisson 方程（在 R 变量中），质量密度等于 (E(2)/4pic(2))，E 表示电场。psi 也满足一个二次线性方程，其中 psi 的算子是拉普拉斯算子的平方根。静电势 Phi (= Q/R)、psi 和曲率张量的所有分量在坐标原点都是有限的。点电荷的电磁能是有限的，等于 (Q(2)/a)。电荷 Q 定义了一个枢轴质量 M() = (Q/G((1/2)))。如果 M < M(*), 那么整个质量都是电磁的。如果 M > M(), 质量 M 的电磁部分 M(em)等于 [M - (M(2) - M(2))((1/2))]，而质量 M 的物质部分 M(mat)等于 (M(2) - M(2))((1/2))。当 M > M(), 根据 Schwarzschild，常数 a 通过将“Schwarzschild 半径”缩小到零来确定。当 M < M(), a 被确定为使引力加速度在原点处为零。
