GUP-Deformed Thermodynamic Behavior of Cylindrical Black Strings in Four Dimensions

We investigate the thermodynamic properties of four-dimensional cylindrically symmetric black strings embedded in an Anti-de Sitter (AdS) spacetime. By incorporating the Generalized Uncertainty Principle (GUP), we introduce minimal length corrections to the thermodynamic framework, thereby capturing quantum gravity effects in the near-horizon regime. We demonstrate that these GUP-induced modifications lead to logarithmic corrections in the entropy-area relation, particularly for small horizon radii, while preserving thermodynamic consistency with the first law of thermodynamics. Through a detailed analysis of the Helmholtz and Gibbs free energies, we observe that the equation of state is significantly deformed by quantum corrections, driving instabilities in black strings with sufficiently small horizon radii. The study of specific heat capacity further confirms a phase transition from stable to unstable configurations, highlighting the role of the minimal length scale on the thermal stability of black string systems.

کلیدواژه ها:

Black Strings ، Thermal Fluctuations ، Logarithmic Entropy ، Black Hole Thermodynamics