Logarithmic F(T) Gravity via Noether Symmetry: A Black Hole Solution and Its Quantum Thermodynamics

In this work, logarithmic teleparallel model, [Formula: see text]=[Formula: see text], previously introduced phenomenologically in the literature, is analytically derived using the Noether symmetry approach within a teleparallel gravity model incorporating a scalar field. Upon substituting the obtained [Formula: see text] function and the scalar field self-interaction potential [Formula: see text] into the field equations, the resulting system is solved analytically, yielding a Schwarzschild–Anti de-Sitter-like black hole solution. Furthermore, it is found that the scalar field exhibits behavior analogous to a cosmological constant in this study. Moreover, within the framework of the Generalized Uncertainty Principle, we compute the quantum gravity corrections to a black hole’s Hawking temperature, specific heat, entropy, and Gibbs free energy, and subsequently analyze the black hole’s local and global thermal stability. The paper also includes graphical analyses and comparisons. The results obtained suggest that quantum gravitational effects may play a significant role in determining the thermal properties of black holes. Finally, the geodesic motion of massless and massive particles in the spacetime of the black hole is investigated. The results show that no stable circular or bound orbits exist in the physically relevant region for either massless or massive particles.