Self-consistency of a Modification Method Based on Membrane Model with Minimal Length Considered

By adopting a result from generalized uncertainty principles (GUP), we modify the inner bound of the membrane model to a physical fixed value and get the cut-offs naturally rather than by hand, which are both in brickwall model and membrane model, and the semi-classical quantization condition could always be valid as well. We also calculate the entropies of Schwarzschild-de Sitter black hole and find the GUP we choose qualitatively shows that the requirement of mass in this method is the same as the natural requirement of the Schwarzschild-de Sitter black hole,which means the method might be self-consistent.