Kiselev/CFT correspondence and black hole thermodynamics

Abstract: In this paper, we study the thermodynamic properties of Kiselev black hole and its holographic dual. We obtain the thermodynamic product formula for the Kiselev black hole. We consider Kiselev Black hole surrounded by both dust and radiation. We find that the area (or entropy) product formula for both cases is mass-independent as well as the case in the Einstein gravity, which interpreted as universal quantity. Moreover, we calculate the black hole entropy bound for both the inner and outer horizons. Furthermore, we show that the central charges of the left and right moving sectors are not the same via universal thermodynamic relations. Such universal relations lead us to calculate the central charge of conformal field theory (CFT). Finally, we see that the left and right of central charge of CFT are same.