Instability of a four-dimensional de Sitter black hole with a conformally coupled scalar field

We study the stability of new neutral and electrically charged four-dimensional black hole solutions of Einstein’s equations with a positive cosmological constant and conformally coupled scalar field [C. Martinez, R. Troncoso, and J. Zanelli, Phys. Rev. D 67, 024008 (2003).]. The neutral black holes are always unstable. The charged black holes are also shown analytically to be unstable for the vast majority of the parameter space of solutions, and we argue using numerical techniques that the configurations corresponding to the remainder of the parameter space are also unstable.