Resonant frequencies of a massless scalar field in the canonical acoustic black hole spacetime
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Resonant frequencies of a massless scalar field in the canonical acoustic black hole spacetime H. S. Vieira1
· V. B. Bezerra2
Received: 28 April 2020 / Accepted: 4 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this work we consider the exact solution of the Klein–Gordon equation describing a massless scalar field in the spacetime of a four dimensional canonical acoustic black hole, which is given in terms of the general Heun function, to investigate the interesting phenomena related to the resonant frequencies. Keywords Klein–Gordon equation · Analogue gravity · General Heun function · Quasispectrum
1 Introduction Even with the recent detection of astrophysical black holes [1,2], it is still extremely difficult to measure some physical phenomena which arise from the interaction between quantum fields and gravitational spacetime backgrounds like compact objects and black holes. In order to overcome these issues, Unruh [3] proposed some analogue models of gravity, where the equation of motion which describes the propagation of sound modes (phonons) on a background hydrodynamic flow (acoustic black hole) can be written as formally identical to the massless Klein–Gordon equation, whose field propagates in a (3 + 1)-dimensional Lorentzian geometry. In this context, in which case gravity can emerge as a phenomenon associated to somed excitations, it would be possible, in principle, to observe in the laboratory some effects which mimic the know phenomena of quantum gravity [4–11].
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H. S. Vieira [email protected] V. B. Bezerra [email protected]
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Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, São Carlos, São Paulo CEP 13560-970, Brazil
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Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, João Pessoa, PB CEP 58051-970, Brazil 0123456789().: V,-vol
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H. S. Vieira, V. B. Bezerra
Since the seminal paper by W. G. Unruh, which opened up this field of research, a lot of investigations in which concern the physics of acoustic black holes was performed, as for example, the Hawking-Unruh radiation from a rotating acoustic black hole [12], the relativistic acoustic metric for a planar black hole [13], the quantum potential in analogue gravity [14], the canonical acoustic thin-shell wormholes [15], and the holographic transport [16]. Among these studies, two are of special interest for us, namely, the work where analytic solutions for massless scalar fields in the both canonical and rotating acoustic black holes are obtained in terms of the Heun’s functions [17,18], and the one about probing the Unruh effect with an accelerated extended system [19]. It is worth point out one important aspect, which comes out from the gravity analogue phenomena associated with these analogue models, that is related to the possibility of using these analogies to try probe and understand some features of quantum field theory in curved spacetime by the realization of accurate experiments. As an ex
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