Newtonian perturbations and the Einstein-Yang-Mills-dilaton equations

TL;DR

This paper demonstrates that establishing the existence of solutions to the static spherically symmetric SU(2) Einstein-Yang-Mills-dilaton equations can be reduced to proving the non-existence of solutions to a related linearized problem, using a Newtonian perturbation approach.

Contribution

It introduces a novel reduction method from a non-linear problem to a linearized problem for EYMd equations using Newtonian perturbations.

Findings

Reduction of non-linear problem to linearized problem

Connection between solution existence and linearized equations

Application of Newtonian perturbation method

Abstract

In this paper we show that problem of proving the existence of a countable number of solutions to the static spherically symmetric SU(2) Einstein-Yang-Mills-dilaton (EYMd) equations can be reduced to proving the non-existence of solutions to the linearized Yang-Mills-dilaton equations (lYMd) satisfying certain asymptotic conditions. The reduction from a non-linear to a linear problem is achieved using a Newtonian perturbation type argument.