Ringing of Reissner–Nordström Black Holes with a Non-Abelian Hair in Gravity’s Rainbow

In this paper, we consider massless scalar perturbations minimally coupled to gravity in the background spacetime of charged black holes in Yang–Mills theory with gravity’s rainbow modification. We calculate the corresponding quasinormal frequencies by employing the sixth-order Wentzel—Kramers—Brillouin (WKB) approximation for both asymptotically flat and de Sitter (dS) spacetimes. We show that the Yang–Mills modification of the Reissner–Nordström black holes leads to an increase in the real and imaginary parts of frequencies. Furthermore, we find that the perturbations in asymptotically flat spacetime decay faster with more oscillations compared to dS spacetime, and we study the effects of the rainbow functions on the oscillations. Interestingly, we reveal a novel feature of this black hole case study and show that, unlike typical black hole solutions such as Schwarzschild, RN, and Kerr, the higher multipole numbers live longer than the lower ones in both asymptotically flat and dS spacetimes. Furthermore, the reflection and transmission coefficients are explored for Einstein–Maxwell–Yang–Mills black holes, and the results are compared for flat and dS asymptotes.