The generalized uncertainty principle effect in acoustic black holes

Abstract: We obtain an effective acoustic metric with quantum corrections that are provided by a minimum length implemented by the generalized Heisenberg uncertainty principle (GUP) in the Abelian Higgs model. The effective acoustic metric now depends on the contribution of scalar and vector potentials. We also explore the Hawking radiation and entropy by considering the effective canonical acoustic black hole and find that the modified Hawking temperature leads to logarithm corrections to the entropy. Finally, we investigate the dispersion relations of the model to establish the relationships among the deviations of the group velocity, frequency and temperature due to the GUP.