The generalized uncertainty principle effect in acoustic black holes

TL;DR

This paper explores how quantum corrections from the generalized uncertainty principle modify acoustic black hole metrics, Hawking radiation, and entropy, revealing logarithmic entropy corrections and altered dispersion relations.

Contribution

It introduces a GUP-based quantum correction to the acoustic metric, analyzing its effects on Hawking radiation, entropy, and dispersion relations in acoustic black holes.

Findings

GUP induces logarithmic corrections to black hole entropy.

Modified Hawking temperature due to GUP affects acoustic black hole properties.

Dispersion relations are altered, affecting group velocity and temperature relationships.

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.