Singularities in Static Spherically Symmetric Configurations of General Relativity with Strongly Nonlinear Scalar Fields

There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions Einstein equations strongly nonlinear scalar field, which allow appearance new type (“spherical singularities”) outside center curvature coordinates. As example, consider field potential ∼sinh(ϕ2n),n>2, grows rapidly for large values. The space-time is assumed to be asymptotically flat. We fulfill numerical investigation different n parameters, define asymptotic properties at spatial infinity. Depending configuration distribution stable circular orbits test bodies around similar case Schwarzschild solution (thus mimicking an ordinary hole), it contains additional rings unstable orbits.