Double instability of Schwarzschild black holes in Einstein-Weyl-scalar theory

TL;DR

This paper investigates the stability of Schwarzschild black holes in Einstein-Weyl-scalar theory, revealing double instabilities due to Gregory-Laflamme and tachyonic effects, leading to scalarized black hole solutions.

Contribution

It identifies the conditions for Ricci-tensor and scalar field instabilities in Schwarzschild black holes within EWS theory, highlighting the double instability mechanism and resulting scalarized solutions.

Findings

Schwarzschild black holes become unstable for $m_2<0.876$ due to Ricci-tensor perturbations.

Tachyonic instability occurs for $m_2<1.174$, leading to multiple scalarized black hole branches.

Double instability involves Gregory-Laflamme and tachyonic modes, affecting black hole stability.

Abstract

We study the stability of Schwarzschild black hole in Einstein-Weyl-scalar (EWS) theory with a quadratic scalar coupling to the Weyl term. Its linearized theory admits the Lichnerowicz equation for Ricci tensor as well as scalar equation. The linearized Ricci-tensor carries with a regular mass term ($m^2_2$), whereas the linearized scalar has a tachyonic mass term ($-1/m^2_2$). It turns out that the double instability of Schwarzschild black hole in EWS theory is given by Gregory-Laflamme and tachyonic instabilities. In the small mass regime of $m_2<0.876$, the Schwarzschild black hole becomes unstable against Ricci-tensor perturbations, while tachyonic instability is achieved for $m_2<1.174$. The former would provide a single branch of scalarized black holes, whereas the latter would induce infinite branches of scalarized black holes.