A Photon Cloud Induced from an Axion Cloud

TL;DR

This work analyzes how an axion cloud around a Kerr black hole induces an EM photon cloud via the axion-photon coupling $k_a$ in first order, within a background EM field described by the extended Wald solution. By solving the coupled system perturbatively and employing the Newman-Penrose and Teukolsky formalisms, the authors show that the induced EM field oscillates at the axion frequency $\, extomega \\approx \, \mu$ and, under the superradiant condition, grows in lockstep with the axion cloud, with no threshold on $k_a$ or the background field amplitude. The induced EM field is dominated by the residential NP component and exhibits symmetries distinct from the background field, including parity properties and quadrupolar structures that may serve as observational signatures of axion-photon coupling and axion clouds near rotating black holes. These results extend classical instability analyses by showing a robust, threshold-free photon cloud generation mechanism in astrophysical Kerr spacetimes and highlight potential polarization or distribution patterns that could trace axion physics in black hole environments.

Abstract

It is known that the axion-photon coupling can lead to quantum stimulated emission of photons and classic exponential amplification of electromagnetic (EM) fields at half the axion mass frequency, when the axion density or the coupling constant is sufficiently large. In this work, we studied the EM photon cloud induced from an axion cloud around a Kerr black hole in the first order of the coupling constant classically. In the presence of a static EM background (like Wald extended solution valid in realistic astrophysical environment), we found that an EM photon cloud emerges, oscillating at the same frequency as the axion cloud and growing exponentially in accordance with the axion cloud when the superradiant condition for the axion field is satisfied. The evolution of the EM photon cloud with time and azimuthal angle is obtained analytically while the cross-sectional distribution is solved numerically. The induced EM field exhibits significantly different symmetries in contrast to the background EM field, which may serve as an indication of the existence of both an axion cloud and axion-photon coupling.

Figures (7)

• Figure 1: The real and imaginal parts of $f_{01M}\left(r_0,\theta\right)$, $f_{11M}\left(r_0,\theta\right)$, $f_{21M}\left(r_0,\theta\right)$ induced from $\phi_1$ are plotted with $a_0=0.5$ and $\alpha=0.1$ in the scale of $200M$, where the superradiant condition is satisfied $\alpha<\frac{a_0}{2r_{\rm h0}}$.
• Figure 2: The components $M^2 F_{\mu\nu}^{\rm cos}{}^*F^{\mu\nu}_{\rm cos},~M^2 F_{\mu\nu}^{\rm sin}{}^*F^{\mu\nu}_{\rm sin},~M^2 F_{\mu\nu}^{\rm cos}{}^*F^{\mu\nu}_{\rm sin}$ of the parity violation term $M^2 F_{\mu\nu}^{(1)}{}^*F^{\mu\nu}_{(1)}$ are plotted with $a_0=0.8$ and $\alpha=0.1,0.2$.
• Figure 3: The components $M^2F_{\mu\nu}^{\rm cos}F^{\mu\nu}_{\rm cos},~M^2 F_{\mu\nu}^{\rm sin}F^{\mu\nu}_{\rm sin},~M^2F_{\mu\nu}^{\rm cos}F^{\mu\nu}_{\rm sin}$ of the contraction of the EM field strength tensor $M^2 F_{\mu\nu}^{(1)}F^{\mu\nu}_{(1)}$ are plotted with $a_0=0.8$ and $\alpha=0.1,0.2$.
• Figure 4: The dimensionless quantities $M E^r_{(1)}$, $M^2 E^\theta_{(1)}$ and $M^2 E^\varphi_{(1)}$ of the induced electric field components are plotted as cosine part and sine part respectively. In all the figures we have set $a_0=0.8$ and $\alpha=0.2$.
• Figure 5: The dimensionless quantities $M B^r_{(1)}$, $M^2 B^\theta_{(1)}$ and $M^2 B^\varphi_{(1)}$ of the induced magnetic field components are plotted as cosine part and sine part respectively. In all the figures we have set $a_0=0.8$ and $\alpha=0.2$.