A note on the black hole thermodynamics

The study of various relations between different quantities is of great importance in thermodynamics. Hence in this paper, we will discuss a specific thermodynamic relation between entropy (S) and temperature (T ) of some of the black holes. Therefore, we will choose Kerr, Kerr-Newman and charged BTZ black holes. Then we will calculate the relations between the thermodynamic quantities and explain the results in detail. Here, we study a special type of duality-like behaviour that occurs in the thermodynamics of black holes while preserving the laws of thermodynamics. The relationship between entropy and temperature is calculated as S_±T_± = γ² for the Kerr and Kerr-Newman black holes and S_±T_± = γ²/4 for the charged BTZ black holes. (author)