Einstein-Yang-Mills Regular Black Holes in Rainbow Gravity

Abstract

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 $λ$ 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 $λ$, 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 $λ$. 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.

Figures (6)

• Figure 1: Hawking temperature as a function of the horizon radius, $r_H$, for some values of the rainbow parameter and the coupling constant, and $Q=1.0$.
• Figure 2: Specific heat as a function of the horizon radius for selected values of the rainbow parameter and the coupling constant, considering $Q=1.0$.
• Figure 3: Left panel: Effective potential of a massless scalar field as a function of $r$ for selected values of the rainbow parameter, with fixed values of $Q = 1.0$, $q = 0.1$, $r_H = 10$, and $\epsilon = \omega = 0.1$. Right panel: Particle emission rate as a function of the particle energy, using the same set of parameters, except for the energy, which is allowed to vary.
• Figure 7: The profile of $\rho^{eff} + p_{r}^{eff} + p_{\theta}^{eff} + p_{\phi}^{eff}$ as distance from the event horizon to $r = 10$ for selected values of the parameter set as $r_H = 5.0, Q = 1.0, q = 0.1$.
• Figure 8: Left panel: Ricci's scalar as a function of $r$, for some values of the rainbow parameter. Right panel: Kretschmann's scalar as a function of $r$ for the same selected values of the rainbow parameter. The remaining parameters are set to $r_H = 5.0$, $Q = 1.0$, and $q = 0.1$.