Black holes with scalar hair: Extending from and beyond the Schwarzschild solution

TL;DR

This paper introduces new scalarized black hole solutions extending from Schwarzschild and Einstein-Weyl gravity, demonstrating thermodynamic preference and evading the no-hair theorem in higher-derivative gravity.

Contribution

It constructs novel scalarized black hole solutions beyond general relativity, directly solving fourth-order equations to expand the known solution space.

Findings

Scalarized black holes are thermodynamically preferred.

Solutions extend from Schwarzschild and Einstein-Weyl gravity.

Evasion of the no-hair theorem in higher-derivative gravity.

Abstract

We construct novel scalarized black hole (BH) solutions beyond the general relativity (GR) framework. These scalarized BH solutions are extended from the Schwarzschild one and the non-Schwarzschild one in the pure Einstein-Weyl gravity. By studying the BH entropy and free energy, we demonstrate that the scalarized BH extending from the Schwarzschild one exhibits thermodynamically preferred. We obtain these novel solutions by directly solving the full fourth-order equations of motion. This narrows the problematic solution space obtained by commonly adopted second-order reduction to physically valid spaces. Our findings also unveil the evasion of the no-hair theorem within the realm of higher-derivative gravity.