Spherically symmetrical configurations of self-dual Yang-Mills and Einstein-Plebanski equations

TL;DR

This paper constructs spherically symmetrical reductions of self-dual Yang-Mills and Einstein-Plebanski equations, revealing known solutions in the Yang-Mills case and introducing new equations and solutions for the Plebanski case.

Contribution

It presents a unified method for spherically symmetrical reductions of both equations, discovering new equations and solutions for the Plebanski system.

Findings

Recovered known solutions for self-dual Yang-Mills equations.

Derived new equations describing spherically symmetrical Plebanski configurations.

Identified particular solutions for the new Plebanski equations.

Abstract

Spherically symmetrical reductions of self-dual Yang-Mills and Einstein-Plebanski equations are constructed at the same manner. As in the first case we come back to known before solutions (under such kind of reduction but in some different form) if in the second one we obtain unknown before equation describing the spherically symmetrical configurations of Plebanski equation and some number of its particular solutions.