Singularities in static spherically symmetric configurations of General Relativity with strongly nonlinear scalar fields

TL;DR

This paper discovers new types of singularities in static, spherically symmetric solutions of Einstein's equations coupled with strongly nonlinear scalar fields, revealing complex orbital structures around these configurations.

Contribution

It introduces static solutions with novel 'spherical singularities' outside the center, expanding understanding of possible relativistic objects with nonlinear scalar fields.

Findings

Existence of solutions with spherical singularities outside the center.

Configurations can mimic black holes or have additional unstable orbit rings.

Numerical analysis for different potentials and parameters.

Abstract

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 of Einstein equations with a strongly nonlinear scalar field, which allow the appearance of singularities of a new type (``spherical singularities'') outside the center of curvature coordinates. As the example, we consider a scalar field potential $\sim$$\sinh(\phi^{2n}),\,n>2$, which grows rapidly for large field values. The space-time is assumed to be asymptotically flat. We fulfill a numerical investigation of solutions with different $n$ for different parameters, which define asymptotic properties at spatial infinity. Depending on the configuration parameters, we show that the distribution of the stable circular orbits of test bodies around the configuration is either similar to that in the case of the Schwarzschild solution (thus mimicking an ordinary black hole), or it contains additional rings of unstable orbits.