Perturbations of massless external fields in a special Horndeski hairy black hole

In this paper, we study the propagations of external fields in a specific black hole solution in Horndeski theory, including the scalar field, electromagnetic field and Dirac field. We extensively explore the quasinormal frequencies, time evolution, greybody factors and emission rates of those massless perturbing fields by solving the corresponding master equations in the specific Horndeski hairy black hole. With the use of both numerical and analytical methods, we disclose the competitive/promotional influences of the Horndeski hair, spin and quantum momentum number of the external fields on those phenomenal physics. Our results show that this specific Horndeski hairy black hole is stable under those perturbations. Moreover, a larger Horndeski hair could enhance the intensity of energy emission rate for Hawking radiation of various particles, indicating that comparing to the Schwarzschild black hole, this specific Horndeski hariy black hole could have longer or shorter lifetime depending on the sign of the Horndeski hair.