Thermodynamics of rotating black hole in the presence of cold dark matter

We have computed the thermodynamic properties of a rotating black holes in the presence of cold dark matter. The dependence of temperaure, Gibbs free energy, specific heat on the horizon radius have been studied for various values of critical density (\r{ho}c ) of the cold dark matter. The studies shows that only small values of critical density of cold the dark matter, black hole are stable.