Quasinormal modes and shadow in Einstein Maxwell power-Yang–Mills black hole

In the present paper, we investigate the quasinormal modes of an Einstein–Maxwell power-Yang–Mills black hole in four dimensions, considering a specific value of the power parameter $p=1/2$. This particular case represents a black hole with both Abelian and Non-Abelian charges and is asymptotically non-flat. We begin by deriving the effective potential for both a neutral massless particle and a neutral Dirac particle using the aforementioned black hole solution. Subsequently, employing the sixth-order WKB approximation method, we calculate the (scalar) quasinormal modes. Our numerical analysis indicates that these modes are stable within the considered parameter range. This result is also confirmed using the eikonal approximation. Furthermore, we calculate the shadow radius for this class of BH and derive constraints on the electric and Yang–Mills charges ($Q,Q_{\mathrm{Y\; M}}$) by using imaging observational data for Sgr A${}^{\star }$, provided by the Event Horizon Telescope Collaboration. We observe that as the electric charge $Q$ increases, the allowed range shifts towards negative values of $Q_{\mathrm{Y\; M}}$. For instance, for the maximum value $Q\approx 1.1$ obtained, the allowed range becomes $-0.171\lesssim Q_{\mathrm{Y\; M}}\lesssim -0.087$ consistent with KECK and VLTI data, while still retaining a non-vanishing horizon.