Modified Hawking radiation of Schwarzschild-like black hole in bumblebee gravity model

In this article, we study the Hawking radiation of the Schwarzschild black hole within the bumblebee gravity model (SBHBGM). Considering classical approaches involving Killing vectors and the standard Hamilton-Jacobi method, the Hawking radiation of SBHBGM is computed. The Painlevé-Gullstrand, ingoing Eddington-Finkelstein, and Kruskal-Szekeres coordinate systems are introduced as alternatives to the naive coordinates, providing insights into gravitational behavior around massive objects like black holes. Incorporating the Generalized Uncertainty Principle (GUP) into the Hamilton-Jacobi equation, a modified equation characterizing particle behavior near the event horizon is obtained. By calculating the tunneling probability using the modified action, the GUP-induced modifications to the emitted particle's behavior are considered, resulting in the derivation of the modified temperature of the SBHBGM. Finally, we study the quantum-corrected entropy of the SBHBGM and discuss the findings with possible future projects.