Dynamical evolution of non-minimally coupled scalar field in spherically symmetric de Sitter spacetimes

TL;DR

This paper studies how a non-minimally coupled scalar field behaves dynamically in de Sitter spacetimes, revealing conditions for stability and instability influenced by field mass, coupling, and black hole charge.

Contribution

It provides a detailed analysis of the stability conditions of scalar fields with non-minimal coupling in de Sitter black hole backgrounds, highlighting new instability regions and stability thresholds.

Findings

Massless scalar fields show unaffected quasinormal modes.

Massive fields exhibit instability regions depending on parameters.

Unstable modes are more prominent for the $ extless$0$>$ angular momentum case.

Abstract

We investigate the dynamical behavior of a scalar field non-minimally coupled to Einstein's tensor and Ricci scalar in geometries of asymptotically de Sitter spacetimes. We show that the quasinormal modes remain unaffected if the scalar field is massless and the black hole is electrically chargeless. In the massive case, the coupling of both parameters produces a region of instability in the spacetime determined by the geometry and field parameters. In the Schwarzschild case, every solution for the equations of motion with $\ell>0$ has a range of values of the coupling constant that produces unstable modes. The case $\ell=0$ is the most unstable one, with a threshold value for stability in the coupling. For the charged black hole, the existence of a range of instability in $\eta$ is strongly related to geometry parameters presenting a region of stability independent of the chosen parameter.