# Kiselev/CFT correspondence and black hole thermodynamics

## TL;DR

This paper explores the thermodynamics and holographic duality of Kiselev black holes, deriving universal entropy relations and calculating the conformal field theory central charges, revealing insights into black hole/CFT correspondence.

## Contribution

It introduces the thermodynamic product formulas for Kiselev black holes surrounded by dust and radiation, and determines the CFT central charges from thermodynamic relations.

## Key findings

- Area (entropy) product is mass-independent, indicating universality.
- Calculated the black hole entropy bounds for inner and outer horizons.
- Found that the left and right CFT central charges are equal.

## 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.