Dilatonic Black Holes in Higher Curvature String Gravity

TL;DR

This paper demonstrates the existence of dilatonic black hole solutions with secondary hair in a 4D superstring effective action including Gauss-Bonnet terms, challenging traditional no-hair theorems.

Contribution

It provides analytical and numerical evidence for black holes with dilaton hair in higher curvature string gravity, expanding understanding beyond classical no-hair results.

Findings

Existence of black hole solutions with dilaton hair.

Dilaton charge is determined by black hole mass.

Solutions avoid naked singularities.

Abstract

We give analytical arguments and demonstrate numerically the existence of black hole solutions of the $4D$ Effective Superstring Action in the presence of Gauss-Bonnet quadratic curvature terms. The solutions possess non-trivial dilaton hair. The hair, however, is of ``secondary" type", in the sense that the dilaton charge is expressed in terms of the black hole mass. Our solutions are not covered by the assumptions of existing proofs of the ``no-hair" theorem. We also find some alternative solutions with singular metric behaviour, but finite energy. The absence of naked singularities in this system is pointed out.