Stable spontaneously-scalarized black holes in generalized scalar-tensor theories

TL;DR

This paper investigates the stability of scalarized black holes in generalized scalar-tensor theories, showing they are radially stable under certain conditions and that Ricci couplings influence the hyperbolicity of perturbation equations.

Contribution

It provides the first analysis of radial stability of scalarized black holes in these theories, highlighting the role of Ricci couplings in stability and hyperbolicity.

Findings

Scalarized black holes are radially stable for specific Ricci couplings.

Ricci coupling reduces the region where hyperbolicity is lost.

Stability conditions align with cosmological and pulsar constraints.

Abstract

It has been shown that the synergy of a scalar field coupling with both the Ricci scalar and the Gauss-Bonnet invariant significantly affects the properties of scalarized black holes and neutron stars, including their domain of existence and the amount of scalar hair they carry. Here we study the radial stability of scalarized black-hole solutions. We demonstrate that they are stable against radial perturbations for Ricci couplings consistent with both a late-time cosmological attractor and the evasion of binary pulsar constraints. In addition, we investigate the effect of the Ricci coupling on the hyperbolicity of the equation governing linear, radial perturbations and show that it significantly reduces the region over which hyperbolicity is lost.