Thermodynamics of rotating Kaluza-Klein black holes in gravity's rainbow

In this paper, a four-dimensional rotating Kaluza Klien (K-K) black hole was deformed using rainbow functions derived from loop quantum gravity and non-commutative geometry. We studied the thermodynamic properties and critical phenomena of this deformed black hole. The deformed temperature and entropy showed the existence of a Planckian remnant. The calculation of Gibbs free energy G for the ordinary and deformed black holes showed that both share a similar critical behaviour.