In this note, we explore a recent proposal on the chaotic behavior of the scalar field in black hole backgrounds. We study details of the spectral form factor of scalar field normal modes corresponding to the rotating BTZ black hole background. We consider the effect of non-zero field mass in its interplay between cutoff parameters and non-zero angular velocity. Besides the canonical spectral form factor, we consider its complex-valued generalizations (generalized spectral form factors) which captures finer details via taking into account higher-level correlations. The three-level generalization of the spectral form factor is calculated showing discrepancies with the RMT result.
Ageev et al. (Mon,) studied this question.