Exterior fields of collapsed bodies

Static spherically symmetric solutions of the Einstein equations (without the cosmological term) and the Schrödinger–Fock–Klein (or Proca) equations with the massive scalar field $\varphi$ (or vector field $B_{\mu}$) in the central coordinate system with the interval $ds^2=e^{\nu}dx^{0\,2} -e^{\lambda}dr^2-r^2d\Omega^2$ are investigated. It is shown that every solution $\{\nu, \lambda, \varphi\}$ $(resp., \{\nu, \lambda, B_{\mu}\})$ with asymptotically flat metrics and $\varphi\not\equiv 0$ $(resp., B_{\mu}\not\equiv 0)$ is regular with respect to $r$ in the interval $(0,\infty)$.