Limiting Behavior of Solutions to the Einstein-Yang/Mills Equations

TL;DR

This paper investigates the limiting behavior of solutions to the Einstein-Yang/Mills equations, showing how their ADM masses converge to specific values depending on the solution type and horizon size.

Contribution

It extends and corrects previous results on the asymptotic behavior of particle-like and black hole solutions in Einstein-Yang/Mills theory.

Findings

ADM masses tend to 2 for particle-like solutions as nodes increase.

Black hole solutions with horizon < 1 have ADM masses approaching 2.

For horizon > 1, ADM masses converge to horizon + inverse of horizon.

Abstract

The ADM masses of particle-like solutions to the Einstein-Yang/Mills Equations tend to 2 as the number of nodes of the solutions increases. The same result is true for black hole solutions with event horizon less than 1. For event horizon $\rho > 1$ the ADM masses converge to $\rho + \rho^{-1} .$ These statements extend and correct ``An Investigation at the Limiting Behavior of Particle-Like Solutions to the Einstein-Yang/Mills Equations and a New black Hole Solutions'', by J. A. Smoller and A. G. Wasserman, in Comm. Math. Phys., 161, 365-389, (1994).