Instability of an "Approximate Black Hole"

TL;DR

This paper demonstrates that a family of static solutions in vacuum Brans-Dicke theory with  are linearly unstable, indicating they are not stable and may serve as critical solutions at the black hole threshold.

Contribution

The study provides the first linear stability analysis of these solutions and combines it with non-linear evolutions to establish their unstable nature.

Findings

Identified an exponentially growing mode for each solution in the family.

Provided numerical evidence of instability through time evolution.

Suggested these solutions act as critical solutions at the black hole threshold.

Abstract

We investigate the stability of a family of spherically symmetric static solutions in vacuum Brans-Dicke theory (with $\omega=0$) recently described by van Putten. Using linear perturbation theory, we find one exponentially growing mode for every member of the family of solutions, and thus conclude that the solutions are not stable. Using a previously constructed code for spherically symmetric Brans-Dicke, additional evidence for instability is provided by directly evolving the static solutions with perturbations. The full non-linear evolutions also suggest that the solutions are black-hole-threshold critical solutions.