Constraints on Quasinormal modes from Black Hole Shadows in regular non-minimal Einstein Yang-Mills Gravity

This work deals with the scalar quasinormal modes using higher order WKB method and black hole shadow in non-minimal Einstein Yang-Mills theory. To validate the results of quasinormal modes, time domain profiles are also investigated. We found that with an increase in the magnetic charge of the black hole, the ring-down gravitational wave increases non-linearly and damping rate decreases non-linearly. The presence of magnetic charge also results in a decrease in the black hole shadow non-linearly. It is found that for large values of the coupling parameter, the black hole changes to a solitonic solution and the corresponding ring-down gravitational wave frequency increases slowly with a decrease in the damping rate. For the solitonic solutions, the shadow is also smaller. The constraints on the model parameters calculated using shadow observations of M87* and Sgr A* and an approximate analytic relation between quasinormal modes and shadow at the eikonal limit is discussed.