On the instabilities of the static, spherically symmetric SU(2) Einstein-Yang-Mills-Dilaton solitons and black holes

TL;DR

This paper proves that the number of odd parity instabilities in the n-th SU(2) Einstein-Yang-Mills-Dilaton soliton and black hole solutions is exactly n, revealing a direct relationship between solution index and instability count.

Contribution

It establishes a precise count of odd parity instabilities for a class of Einstein-Yang-Mills-Dilaton solutions, advancing understanding of their stability properties.

Findings

Number of odd parity instabilities equals the solution index n.

Instability count directly correlates with the solution's position in the solution sequence.

Provides a rigorous proof linking solution properties to stability characteristics.

Abstract

We prove that the number of odd parity instabilities of the n-th SU(2) Einstein-Yang-Mills-Dilaton soliton and black hole equals n.