Superposition of Weyl solutions: The equilibrium forces

TL;DR

This paper explores superimposed Weyl solutions in Einstein's equations, analyzing equilibrium forces and singular structures like struts, with detailed study of configurations such as a ring and a particle.

Contribution

It introduces explicit superpositions of static axially symmetric bodies in Einstein's equations, analyzing the resulting singular structures and forces, including a detailed case of a ring and a particle.

Findings

Force calculations for various configurations

Identification of singular structures like struts and membranes

Detailed analysis of ring and particle superposition

Abstract

Solutions to the Einstein equation that represent the superposition of static isolated bodies with axially symmetry are presented. The equations nonlinearity yields singular structures (strut and membranes) to equilibrate the bodies. The force on the strut like singularities is computed for a variety of situations. The superposition of a ring and a particle is studied in some detail