Acoustic black holes: massless scalar field analytic solutions and analogue Hawking radiation

Abstract

We obtain the analytic solutions of the radial part of the massless Klein–Gordon equation in the spacetime of both three dimensional rotating and four dimensional canonical acoustic black holes, which are given in terms of the confluent Heun functions. From these solutions, we obtain the scalar waves near the acoustic horizon. We discuss the analogue Hawking radiation of massless scalar particles and the features of the spectrum associated with the radiation emitted by these acoustic black holes.

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Acknowledgments

The authors would like to thank Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for partial financial support.

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Correspondence to H. S. Vieira.

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Vieira, H.S., Bezerra, V.B. Acoustic black holes: massless scalar field analytic solutions and analogue Hawking radiation. Gen Relativ Gravit 48, 88 (2016). https://doi.org/10.1007/s10714-016-2082-x

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Keywords

  • Massless Klein–Gordon equation
  • Rotating acoustic black hole
  • Canonical acoustic black hole
  • Confluent Heun function
  • Black body radiation