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 also calculate the lower bound for the greybody 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 have investigated the black hole shadow and shown that its radius can either increase or decrease as quantum gravity effects become more pronounced, depending on the specific parameter configuration. This behavior suggests that black hole shadow observations may offer a promising avenue for testing the phenomenological implications of 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.