Geometric Hawking radiation of Schwarzschild Black Hole with novel quantum algebra

In the context of an extended General Relativity theory with boundary terms included, we introduce a new nonlinear quantum algebra involving a quantum differential operator, with the aim to calculate quantum geometric alterations when a particle is created in the vicinity of a Schwarzschild black-hole by the Hawking radiation mechanism. The boundary terms in the varied action give rise to modifications in the geometric background, which are investigated by analyzing the metric tensor and the Ricci curvature within the framework of a renormalized quantum theory of gravity.