Einstein-Yang-Mills Regular Black Holes in Rainbow Gravity

In this work, we investigate regular black hole solutions in nonminimal Einstein-Yang-Mills theory modified by Rainbow Gravity, focusing on the impact of quantum gravity effects on their thermodynamics, particle emission, energy conditions, curvature, and shadow formation. We find that the rainbow parameter $\lambda$ alters Hawking's temperature, entropy, and specific heat, leading to modified phase transitions and the possible formation of remnants. We calculate the graybody factor demonstrating that particle emission is enhanced with increasing $\lambda$, reflecting the behavior of the temperature and confirming the impact of the rainbow parameter on the evaporation process. Energy conditions are violated inside the black hole, with violations intensifying for larger $\lambda$. We also show that Rainbow Gravity mitigates singularity formation by softening the curvature near the origin, contributing to the regularity of the solution. Finally, we study the black hole shadow and demonstrate that its radius decreases as quantum gravity effects strengthen, suggesting potential observational tests for Rainbow Gravity. These results highlight the role of Rainbow Gravity in modifying black hole physics and provides a framework for exploring quantum gravitational corrections in astrophysical scenarios.