Thermodynamics of Bardeen regular black hole with generalized uncertainty principle

This study explores the emission of massive charged spin-1 particles from the background of Bardeen regular spacetime by the semi-classical method used to study the Hawking radiation spectrum. We employed the Hamilton-Jacobi method and Wentzel-Kramers-Brillouin approximation technique with the suitable form of the wave function to solve the Proca field equation. We calculated the tunneling probability of outgoing spin-1 particles and the corresponding thermodynamic temperature. Furthermore, we obtained the modified thermodynamic quantities like temperature, entropy as well as heat capacity by utilizing the quadratic form of generalized uncertainty principle (GUP) and minimal length. In the end, we investigated the local stability as well as phase transitions of the Bardeen black hole in the context of GUP-modified heat capacity.