Non-minimally coupled multi-scalar black holes

TL;DR

This paper investigates static, spherically symmetric black hole solutions in a non-minimally coupled multi-scalar theory, revealing a new extremality constraint and stable solutions that violate traditional no-hair theorems.

Contribution

It introduces numerical solutions for multi-scalar black holes under a specific charge constraint, showing deviations from standard extremality conditions and proving their linear stability.

Findings

Existence of numerical black hole solutions under a charge constraint.

Identification of a new extremality condition different from  = 0.

Solutions violate no-hair theorems and are linearly stable.

Abstract

We study the static, spherically symmetric black hole solutions for a non-minimally coupled multi-scalar theory. We find numerical solutions for values of the scalar fields when a certain constraint on the maximal charge is satisfied. Beyond this constraint no black hole solutions exist. This constraint therefore corresponds to extremal solutions, however, this does not match the \kappa = 0 constraint which typically indicates extremal solutions in other models. This implies that the set of extremal solutions have non-zero, finite and varying surface gravity. These solutions also violate the no-hair theorems for N>1 scalar fields and have previously been proven to be linearly stable.