Abstract
We study the stability of topological black holes in the presence of a cosmological constant and a scalar field coupled to the Gauss-Bonnet (GB) term in the extended scalar-tensor theories. We find two competing effects. As the strength of the coupling of the scalar field to the GB term is increasing, the matter is interacting more strongly with gravity while as the hyperbolicity of spacetime is getting larger the kinetic effects of matter tend to dominate. Calculating both analytically and numerically the quasinormal modes (QNMs) we found for each a critical value of , below which there is an instability. When the coupling constant is getting very large, all of the QNMs develop a positive imaginary part indicating an instability. This behavior indicates a phase transition to a scalarized topological black hole induced by curvature effects.
1 More- Received 18 February 2022
- Accepted 14 April 2022
DOI:https://doi.org/10.1103/PhysRevD.105.104039
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