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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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