Thermodynamic Functions of Kerr Black Holes Using Hamiltonian Equation

This paper focuses on calculating key thermodynamic functions—temperature, internal energy, enthalpy, and Helmholtz free energy—of uncharged rotating black holes using the Hamiltonian equation. Analytical mechanics methods, paired with general relativity and thermodynamics, are employed to predict the behavior of these functions by studying the motion of charged particles near a Kerr black hole. The calculations were conducted using Mathematica, providing precise results along with graphical representations of the thermodynamic functions. Planck units are used throughout the analysis to simplify the equations. The findings align with the behavior predicted by Hawking radiation, as both follow similar patterns, suggesting a deeper connection between black hole thermodynamics and radiation. This paper offers a theoretical framework to understand how thermodynamic functions behave within black holes, contributing valuable insights into the role of thermodynamic principles in describing the dynamic properties of black hole systems and enhancing our understanding of black hole physics. shedding light on the variability of this method.