Entropy bound and EGUP correction of d-dimensional Reissner–Nordström black hole in rainbow gravity

Abstract

Inspired by the pronounced effect of gravity’s Rainbow on black hole thermodynamics, entropy relations and bounds have been investigated for [Formula: see text]-dimensional Reissner–Nordström (RN) black hole in the framework of Rainbow gravity. Basic thermodynamic properties of the black hole have been derived for the event horizon and Cauchy horizon. Except for the horizon radius, they all crucially depend on the Rainbow functions. Bounds of the aforesaid thermodynamic quantities have been deduced for both horizons. Analyzing the specific heat capacity, stability conditions have been obtained. Also, the extremal phase of the black hole has been explored. Further, a comparative study has been carried out to distinguish between the effects of Rainbow gravity model parameters on the entropy bound by considering different Rainbow gravity functions. For massless scalar perturbation, quasinormal modes have been computed using modified WKB approach. We have investigated the quantum correction of the black hole in a Rainbow gravity background to obtain the effects of Extended Uncertainty Principle (EUP) and Generalized Uncertainty Principle (GUP) parameters. We have derived the Hawking temperature, specific heat, entropy and remnant masses of the black hole in the Extended General Uncertainty Principle (EGUP) framework, and with the help of graphical methods, we have compared our findings.