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 Painleve-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. We thus examine whether Hawking radiation's temperature depends on the chosen coordinate system or not. 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. In conclusion, we explore the quantum-adjusted entropy of SBHBGM and its associated temperature and assess the findings we have acquired.