Acceleration Radiation of Freely Falling Atoms in Bardeen Regular Black Hole Spacetimes

Abstract

Motivated by the work of Scully \textit{et al.} [ \textcolor{blue}{Proc. Nat. Acad. Sci. 115, 8131 (2018)}] and Camblong \textit{et al.}[ \textcolor{blue}{Phys. Rev. D 102, 085010 (2020)}], we investigate horizon-brightened acceleration radiation (HBAR) for freely falling two-level atoms in the geometry of a Bardeen regular black hole. Building on the quantum-optics approach to acceleration radiation and its near-horizon conformal quantum mechanics (CQM) structure, we show that the dominant physics is again governed by an inverse-square potential in the radial Klein-Gordon equation, with an effective coupling fixed by the Bardeen surface gravity. Using geodesic expansions and a near-horizon CQM reduction of the scalar field, we derive the excitation probability for atoms falling through a Boulware-like vacuum in the presence of a stretched-horizon mirror. The resulting spectrum is Planckian in the mode frequency, with a temperature determined by the Bardeen Hawking temperature. We analyze how the regular core parameter controls the strength of the radiation and demonstrate that the excitation probability is strongly suppressed as the geometry approaches the extremal (cold remnant) limit. Numerical results illustrate the dependence of the spectrum on the Bardeen parameter and on the atomic transition frequency.

Figures (4)

• Figure 1: Dependence of the horizon radius $r_g$ on Bardeen parameter $g$.
• Figure 2: The dependence of the radiation intensity $P_{exc}$ on the mode frequencies $\nu$ for different values of the Bardeen parameter $g$ (top left panel) and for different values of the atomic frequency $\omega$ (upper right panel). The radiation intensity $P_{exc}$ as a function of the Bardeen parameter $g$ for different values of the $\nu$ (bottom left panel) and $\Delta P=P(0)-P(g)$ as a function $\nu$ (bottom right panel). Here we take $g_c=10^{-3}$.
• Figure 3: Radiation intensity $P_{\rm exc}$ plotted against mode frequencies $\nu$ and Bardeen parameter $g$ in 3 dimensions.
• Figure 4: Dependence of the Hawking temperature $T_H^{(B)}$ on the Bardeen parameter $g$ (left plot) and dependence of the wavelength ($\lambda/l_p$) on the mass ($M/m_p$) of the black hole (right plot) from the Wien’s displacement law . Here $l_p$ and $m_p$ indicate the Planck length and Planck mass respectively.