Kiselev/CFT Correspondence and Black Hole Thermodynamics

In this research, we comprehensively investigate the thermodynamic properties of the Kiselev black hole and its holographic counterpart. Our investigation yields the thermodynamic product relations for the Kiselev black hole in environments permeated by dust and radiation. We establish that similar to Einstein’s gravity scenarios, the product of area (or entropy) in both contexts retains mass independence, suggesting its potential universality. In addition, we deduce bounds for the black hole’s entropy at both the inner and outer horizons. We also unveil an asymmetry between the central charges of the left and right-moving sectors when placed within the framework of universal thermodynamic principles. This asymmetry paves the way for inferring the central charges in the associated conformal field theory (CFT). Contrary to our initial findings, we observe that the central charges for the left and right-moving sectors in the CFT ultimately conform to uniform values.