Charged qOS-extremal black hole and its scalarization by entropy function approach

TL;DR

This paper studies the scalarization of charged extremal black holes within Einstein-Gauss-Bonnet-scalar theory, identifying scalar clouds and analyzing entropy to determine the preferred black hole branch.

Contribution

It introduces a new analysis of scalarization in charged extremal black holes using the entropy function approach, revealing scalar clouds and branch preferences.

Findings

Two scalar clouds for positive and negative coupling constants.

The positive branch of scalarized black holes is thermodynamically preferred.

Entropy calculation confirms the stability of the positive branch.

Abstract

We investigate scalarization of charged quantum Oppenheimer-Snyder extremal (cqOSe)-black hole in the Einstein-Gauss-Bonnet-scalar theory with a nonlinear electrodynamics term. This black hole is described by quantum parameter $\alpha$ and magnetic charge $P$. It is equivalent to the qOS-extremal black hole whose action is still unknown when imposing a relation of $(3\alpha P^2)^{1/4}\to 3M/2$. Focusing on the onset of scalarization, we find the single branch of scalarized cqOS extremal (scqOSe)-black holes. To obtain a scalar cloud (seed) for the single branch, however, we have to consider its near-horizon geometry of the Bertotti-Bobinson (BR) spacetime. In this case, two scalar clouds for positive and negative coupling constant $\lambda$ are found to represent two branches. Applying Sen's entropy function approach to this theory, we obtain the entropy which is the only physical quantity to describe the scqOSe-black holes. We find that the positive branch is preferred than the negative branch.