Thermal stability of black hole in bumblebee gravity with cosmological constant.

This paper delves into the intriguing topic of the thermal stability of black holes (BHs) in the unique framework of bumblebee gravity. Our analysis primarily focuses on thermodynamic stability by examining the event horizon, black hole mass, thermal temperature and heat capacity. Additionally, we explore the intricacies of thermodynamic geometries such as Ruppeiner and Weinhold formulations and calculate their respective scalar curvatures in the context of bumblebee gravity. In our investigation, we also delve into the concept of phase transition through Gibbs free energy and the fascinating phenomenon of BH evaporation by energy emission. This research provides valuable insights into the complex thermodynamic properties of BHs and enhances our understanding of bumblebee gravity. We study the bosonic tunneling with spin-1 tunneling radiation in BHs. Initially, the generalized uncertainty principle (GUP) was used to correct the field equation (FE) for vector particles with spin-1 and demonstrate that the Hawking temperature rises with an improvement in the GUP and the radial component of the vector field but is unaffected by the radial components. [ABSTRACT FROM AUTHOR]