Effects of stimulated emission and superradiant growth of non-spherical axion cluster

Abstract: We explore the stimulated emission of photons in non-spherical axion clusters with or without the axion source from the superradiance of a rotating black hole (BH). In particular, we focus on the cluster with the initial axion distribution in the $(l,m)=(1,1)$ mode which mimics the shape of an axion cloud induced by the BH superradiance. After establishing the hierarchy of Boltzmann equations governing a general non-spherical axion-photon system, we examine the evolution of photon and axion distributions in the cluster and possible stimulated emission signals. In the case without the axion source, the resultant signal would be a single photon pulse. As for the system with the BH superradiance as the axion source, multiple pulses are predicted. We also show that, for the latter case, the combined effects of stimulated emissions and the axion production from the BH superradiance could reach a balance where the axion cluster becomes uniformly and spherically distributed. Due to the energy and temporal characteristics of the obtained pulses, we demonstrate that the stimulated emissions from the axion cluster with axions sourced by the BH superradiance provide a candidate explanation to the observed fast radio bursts.