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This paper presents a numerical investigation into superradiance and Hawking radiation for a specific rotating acoustic black hole model, characterized by parameters $A$ and $B$, within the framework of analogue gravity. The standard radial wave equation for scalar perturbations in the effective metric of this model is solved numerically using an adaptive Runge-Kutta method with tortoise coordinates; this approach necessitates careful numerical inversion of the coordinate transformation near the horizon via a root-finding algorithm. By imposing appropriate boundary conditions, we extract the reflection coefficient $\mathcal{R}$ and transmission coefficient $\mathcal{T}$ across a range of frequencies $\omega$. Our results clearly demonstrate superradiance, with the reflectivity $|\mathcal{R}|^2$ exceeding unity for $\omega < m\Omega_H = 1$ (where $m=-1$ and $\Omega_H=-1$), which confirms energy extraction from the rotating background. The high accuracy of our method is validated by the flux conservation relation, $|\mathcal{R}|^2 + [(\omega - m\Omega_H)/\omega]|\mathcal{T}|^2 = 1$, which typically holds to a numerical precision of $10^{-8}$. Furthermore, using the derived Hawking temperature and the Bose-Einstein distribution modified for rotation, we calculate the Hawking radiation power spectrum $P_\omega$, incorporating the numerically obtained transmission coefficient $|\mathcal{T}|^2$ as the model's greybody factor. \myaddedblue{A prominent feature of $P_\omega$ is its sharp enhancement (or divergence) as $\omega$ approaches the threshold $m\Omega_H$ from above, a characteristic directly linked to the denominator of the Bose-Einstein factor. The research also reveals that superradiant amplification and Hawking spectrum characteristics are significantly dependent on the specific values of flow parameters $A$ and $B$, even when the superradiant threshold $m\Omega_H$ remains unchanged. This detailed numerical study provides quantitative results for the scattering and radiation properties of this model, offering robust support for the analogue gravity framework.
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Keywords:
- Acoustic black hole /
- Superradiance /
- Hawking radiation /
- Numerical calculation
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[1] Hawking S W 1974 Nature 248 30.
[2] Unruh W G 1981 Phys. Rev. Lett. 46 1351.
[3] Li C A 2000 Acta Phys. Sin. 49 (李传安 2000 物理学报 49 1648) 1648.
[4] Visser M 1998 Class. Quantum Grav. 15 1767.
[5] Barceló C, Liberati S, Visser M 2005 Living Rev. Relativ. 8 12.
[6] Steinhauer J 2016 Nature Phys. 12 959.
[7] Ge X H, Sin S J 2010 J. High Energy Phys. 2010 087.
[8] Wang Q B, Ge X H 2020 Phys. Rev. D 101 084014.
[9] Ge X H, Nakahara M, Sin S J, Tian Y, Wu S F 2019 Phys. Rev. D 99 104047.
[10] Ge X H, Sun J R, Tian Y, Wu X N, Zhang Y L 2015 Phys. Rev. D 92 084052.
[11] Yuan H, Ge X H 2022 Eur. Phys. J. C 82 566.
[12] Ge X H, Wu S F, Wang Y, Yang G H, Shen Y G 2012 Int. J. Mod. Phys. D 21 1250038.
[13] Penrose R 1969 Riv. Nuovo Cimento 1 252.
[14] Zel’dovich Y B 1971 JETP Lett. 14 180.
[15] Starobinsky A A 1973 Sov. Phys. JETP 37 28.
[16] Misner C W 1972 Bull. Am. Phys. Soc. 17 472.
[17] Basak S, Majumdar P 2003 Class. Quantum Grav. 20 3907.
[18] Yu M H, Ge X H 2023 Phys. Rev. D 107 026013.
[19] Yu M H, Ge X H 2022 Eur. Phys. J. C 82 985.
[20] Yu M H, Ge X H, Lu C Y 2023 Eur. Phys. J. C 83 87.
[21] Ge X H 2025 Acta Phys. Sin. 74 (葛先辉 2025 物理学报 74 081101-1) 081101-1.
[22] Fang H Z, Zhou K H, Song Y M 2013 Acta Phys. Sin. 32(方恒忠,周开虎,宋玉明 2013 大学物理 32 30) 30.
[23] Zhao R, Zhang L C, Li H F 2008 Acta Phys. Sin. 57 (赵仁,张丽春,李怀繁 2008 物理 学报 57 7463) 7463.
[24] Zhao R, Zhang L C, Li H F 2010 Acta Phys. Sin. 59 (赵仁,张丽春,李怀繁 2010 物理 学报 59 2982) 2982.
[25] Nam S, Park J D 2009 Class. Quantum Grav. 26 145015.
[26] Demirkaya B, Dereli T, Güven K 2020 Phys. Scr. 95 055001.
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