Quantum geometric corrections from GUP and noncommutativity to Hawking radiation in the BTZ black hole

In this paper, we develop a unified semiclassical framework to quantify quantum-geometric corrections to the Hawking temperature of the (2+1)-dimensional BTZ black hole arising from noncommutative geometry and the Generalized Uncertainty Principle (GUP). The GUP correction is implemented through a perturbative deformation of the Hamilton–Jacobi tunneling structure, whereas noncommutative effects are introduced through a Seiberg–Witten deformation of the BTZ geometry. By using the WKB approximation applied to the GUP-modified Dirac equation (and its scalar analogue), we obtain analytical expressions for the corrected radial action and derive a common spin-independent first-order shift for the two field sectors considered. Noncommutative contributions appear at order [Formula: see text] through the Seiberg–Witten map, while GUP corrections depend on a geometric combination of the particle mass and angular momentum. Within the perturbative regime, the GUP correction suppresses the BTZ temperature, while the noncommutative correction produces a controlled temperature shift whose sign is governed by the coefficient [Formula: see text]. The results provide a mathematically coherent bridge between minimal length deformations, noncommutative geometry, and lower dimensional black hole thermodynamics.