Dilatonic Black Holes in Higher-Curvature String Gravity II: Linear Stability

TL;DR

This paper proves the linear stability of dilatonic black holes in a higher-curvature string gravity theory, showing they are stable solutions that challenge the traditional no-hair conjecture, with the dilaton hair being secondary.

Contribution

It provides a rigorous proof of linear stability for dilatonic black holes in a string-inspired higher-derivative gravity model, a novel result in the field.

Findings

Dilatonic black holes are linearly stable.

The stability proof uses a Schrödinger problem mapping.

These black holes bypass the no-hair conjecture.

Abstract

We demonstrate linear stability of the dilatonic Black Holes appearing in a string-inspired higher-derivative gravity theory with a Gauss- Bonnet curvature-squared term. The proof is accomplished by mapping the system to a one-dimensional Schrodinger problem which admits no bound states. This result is important in that it constitutes a linearly stable example of a black hole that bypasses the `no-hair conjecture'. However, the dilaton hair is `secondary'in the sense that it is not accompanied by any new quantum number for the black hole solution.