Non-Linear Equation Approach to Black Hole Phase Transitions

Document Type : Research Article

Author

Department of General \& Theoretical Physics, L. N. Gumilyov Eurasian National University, Astana, 010008, Kazakhstan

Abstract

We investigate the role of non-linear equations in characterizing black hole phase transitions within extended thermodynamic frameworks. By formulating the critical conditions as the solution of a non-linear equation derived from the equation of state, we provide an analytical and numerical study of black hole thermodynamics near criticality. Our analysis demonstrates that the non-linear structure encodes universal behavior analogous to the Van der Waals fluid, and it offers a systematic way of locating transition points. The method extends naturally to higher-dimensional and charged AdS black holes, highlighting the generality of this approach.

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