The Spectroscopy of the 2+1 Dimensional Analog Black Hole in Photon-Fluid Model

Abstract: In this paper, we explore quasibound states (QBS), scalar cloud, Hawking radiation, superradiance, and greybody factor of relativistic massive phonon modes in a photon-fluid rotation black hole. We investigate quasibound states and scalar clouds using exact eigensolutions to the analog Klein-Gordon equation in the analog black hole background and revisit the Wentzel-Kramers-Brillouin (WKB) upper bound on the scalar clouds' energy ratio. Using the obtained exact radial solution, we use the Damour-Ruffini method to calculate the power spectrum of the analog black hole's Hawking radiation. We then use the analytical asymptotic matching technique (AAM) to investigate the analog black hole's superradiance for low energy massive photon scattering, resulting in the analytical amplification factor and the greybody factor formulas of the analog black hole. We discover that the analog black hole in the photon-fluid model is superradiant with an energy range of $\varpi < \omega<m_\ell\Omega_H$. As a result, the greybody factors are negative for co-rotating modes in the superradiant regime.