Purely metric Horndeski theories and spontaneous curvaturization of black holes

TL;DR

This paper investigates a class of metric theories of gravity with a scalar field, revealing a phenomenon called curvaturization where small Kerr black holes develop scalar-induced curvature growth, leading to new black hole solutions.

Contribution

It identifies a subclass of purely metric Horndeski theories where scalarization causes black holes to undergo spontaneous curvature growth, introducing novel black hole solutions.

Findings

Scalar field causes tachyonic instability in small Kerr black holes.

Curvaturization leads to new black hole solution branches.

Properties of static and spinning black holes are characterized.

Abstract

We explore purely metric theories of gravity with second-order equations of motion and a single additional, purely gravitational, propagating, scalar degree of freedom. We identify a subclass of these theories in which this scalar causes a phenomenon similar to black-hole scalarization, which we call curvaturization: around small enough Kerr black holes, the scalar induces a tachyonic instability. This triggers a sudden growth of Ricci curvature and results in a new branch of vacuum black-hole solutions. We study the properties of these black holes both in the static as well as the spinning case.