Acoustic regular black hole in fluid and its similarity and diversity to a conformally related black hole

Abstract

We address an interesting question in the present paper that whether the acoustic gravity can be applied as a tool to the study of regular black holes. For this purpose, we construct a general acoustic regular black hole in the spherically symmetric fluid, where its regularity is verified from the perspective of finiteness of curvature invariants and completeness of geodesics. In particular, we find that the acoustic interval not only looks like a line element of a conformally related black hole in which the fluid density can be regarded as a conformal factor, but also gives rise to a non-vanishing partition function which coincides with that of a conformally related black hole. As an application, we provide a specific acoustic regular black hole model, investigate its energy conditions and compute its quasinormal modes. We note that the strong energy condition of our model is violated completely outside the horizon of the model but remains valid in some regions inside the horizon, which may give a new insight into the relation between the regularity and strong energy condition. Moreover, we analyze the oscillating and damping features of our model when it is perturbed.