Scalar perturbation around a rotating Kalb-Ramond BTZ black hole

Abstract: We investigate the scalar perturbation of a newly proposed Kalb-Ramond (KR) BTZ-like black hole. After the separation of variables for the Klein-Gordon equation, we find that the radial part reduces to the general Heun equation. Using the Heun function, we compute quasinormal modes (QNMs) subject to generic Robin boundary conditions, which shows that the KR parameter substantially modifies the QNM spectrum and only the fundamental mode on the left branch has an instability. To ascertain whether the instability is superradiant, we further analyze how the KR field changes the energy and angular momentum fluxes. Our results show that the KR parameter shifts the threshold and the range of the Robin coupling parameter where the superradiance occurs, underscoring the importance of the KR field in modeling black hole perturbations.