Higher dimensional black hole scalarization

TL;DR

This paper explores the phenomenon of scalarization in higher-dimensional black holes within scalar-tensor theories, revealing new solutions and properties that differ from four-dimensional cases, and relating different models through conformal transformations.

Contribution

It provides the first explicit constructions of scalarized black holes in higher dimensions and compares different scalarization mechanisms across models.

Findings

Scalarization occurs in higher-dimensional black holes, unlike in four dimensions.

Explicit solutions for scalarized black holes in 5, 6, and 8 dimensions are constructed.

The models are related via conformal transformations, linking Ricci scalar coupling to Maxwell invariant coupling.

Abstract

In the simplest scalar-tensor theories, wherein the scalar field is non-minimally coupled to the Ricci scalar, spontaneous scalarization of electrovacuum black holes (BHs) does not occur. This ceases to be true in higher dimensional spacetimes, $d>4$. We consider the scalarization of the higher dimensional Reissner-Nordstr\"om BHs in scalar-tensor models and provide results on the zero modes for different $d$, together with an explicit construction of the scalarized BHs in $d=5$, discussing some of their properties. We also observe that a conformal transformation into the Einstein frame maps this model into an Einstein-Maxwel-scalar model, wherein the non-minimal coupling occurs between the scalar field and the Maxwell invariant (rather than the Ricci scalar), thus relating the occurence of scalarization in the two models. Next, we consider the spontaneous scalarization of the Schwarzschild-Tangherlini BH in extended-scalar-tensor-Lovelock gravity in even dimensions. In these models, the scalar field is non-minimally coupled to the $(d/2)^{th}$ Euler density, in $d$ spacetime dimensions. We construct explicitly examples in $d=6,8$, showing the properties of the four dimensional case are qualitatively generic, but with quantitative differences. We compare these higher $d$ scalarized BHs with the hairy BHs in shift-symmetric Horndeski theory, for the same $d$, which we also construct.