Acoustic black hole in Schwarzschild spacetime: quasi-normal modes, analogous Hawking radiation and shadows

Abstract: Various properties of acoustic black holes constructed in Minkowski spacetime have been widely studied in the past decades. Recently the acoustic black holes in general spacetime were proposed . In this paper, we first investigate the basic characteristics of `curved' acoustic black hole in Schwarzschild spacetime, including the quasi-normal modes, grey-body factor and analogous Hawking radiation. We find that the signal of quasi-normal mode is weaker than that of Schwarzschild black hole. Moreover, as the tuning parameter increases, both the positive real part and negative imaginal part of the quasi-normal frequency approach to the horizonal axis, but they will not change sign. This means that all the perturbations could die off and the system is stable under those perturbations. Since the larger tuning parameter suppresses the effective potential barrier, so it enhances the grey-body factor. The energy emission rate of Hawking radiation does not monotonically increase of the tuning parameter because of the non-monotonicity of the Hawking temperature. Finally, as a first attempt, we study the acoustic black hole shadow. The radius of acoustic shadow becomes larger as the tuning parameter increases, because both the related acoustic horizon and the acoustic sphere become larger. Our studies could help us to further understand the near horizon geometrical features of the black hole. We also expect that our observations could be detected experimentally in the near future.