Stability and quasinormal modes for black holes with time-dependent scalar hair

TL;DR

This paper studies the stability and quasinormal modes of black holes with time-dependent scalar hair in scalar-tensor theories, revealing potential observational signatures in gravitational wave data.

Contribution

It introduces a new exact black hole solution with non-constant scalar kinetic term and analyzes its stability and quasinormal mode spectrum.

Findings

Identified stability bounds for the new solution.

Predicted shifts in quasinormal mode frequencies and damping times.

Forecasted gravitational wave constraints on the model parameter.

Abstract

We investigate black hole solutions with time-dependent (scalar) hair in scalar-tensor theories. Known exact solutions exist for such theories at the background level, where the metric takes on a standard GR form (e.g. Schwarzschild-de Sitter), but these solutions are generically plagued by instabilities. Recently, a new such solution was identified in arXiv:2310.11919, in which the time-dependent scalar background profile is qualitatively different from previous known exact solutions - specifically, the canonical kinetic term for the background scalar $X$ is not constant in this solution. We investigate the stability of this new solution by analysing odd parity perturbations, identifying a bound placed by stability and the resulting surviving parameter space. We extract the quasinormal mode spectrum predicted by the theory, identifying a shift of quasinormal mode frequencies and damping times compared to GR. We forecast constraints on these shifts (and the single effective parameter $\hat\beta$ controlling them) from current and future gravitational wave experiments, finding constraints at up to the ${\cal O}(10^{-2})$ and ${\cal O}(10^{-6})$ level for LVK and LISA/TianQin, respectively. All calculations performed in this paper are reproducible via a companion Mathematica notebook.