Superradiant energy extraction from rotating hairy Horndeski black holes

Abstract: Adopting the manifest of low-frequency and low mass for the scalar perturbation, we perform a semi-classical analysis of the superradiance phenomenon for a rotating hairy Horndeski black hole (BH). For the spacetime under study enriched by the hairy Horndeski parameter $h$, in addition to the mass $M$ and spin $a$, we compute the amplification factor of scalar wave scattering indicating the energy extraction from the BH. We find that due to the addition of the hairy parameter $h$ in the geometry, the superradiance scattering and its frequency range enhance compared to the Kerr BH. This implies that Horndeski's gravity belongs to those alternative theories of gravity that make the amplification factor larger than the Kerr BH so that the energy extraction in its framework is more efficient than general relativity. Calculating the outgoing energy flux measured by an observer at infinity verifies the role of the hairy parameter $h$ in the increase of energy extraction efficiency from the rotating BH. By implementing the BH bomb mechanism, we present an analysis of the superradiant instability of the underlying BH spacetime against massive scalar fields. Our analysis indicates that the hairy Horndeski parameter leaves no imprint on the standard superradiant instability regime.