Ergoregion instability and echoes for braneworld black holes: Scalar, electromagnetic, and gravitational perturbations

In the context of the higher dimensional braneworld scenario, we have argued that the occurrence of horizonless exotic compact objects, as an alternative to classical black holes, is more natural. These exotic compact objects carry a distinctive signature of the higher dimension, namely a tidal charge parameter, related to the size of the extra dimension. Due to the absence of any horizon, rotating exotic compact objects are often unstable because of superradiance. Interestingly, these higher dimensional exotic compact objects are more stable than their four-dimensional counterpart, as the presence of the tidal charge reduces the size of the extra dimension and hence results in a stronger gravitational field on the brane. A similar inference is drawn by analyzing the static modes associated with these exotic compact objects, irrespective of the nature of the perturbation, i.e., it holds true for scalar, electromagnetic and also gravitational perturbation. The postmerger ringdown phase of the exotic compact object in the braneworld scenario, which can be described in terms of the quasinormal modes, holds a plethora of information regarding the nature of the higher dimension. In this connection we have discussed the analytical computation of the quasinornial modes as well as their numerical estimation for perturbations of arbitrary spin, depicting existence of echoes in the ringdown waveform. As we have demonstrated, the echoes in the ringdown waveform depend explicitly on the tidal charge parameter and hence its future detection can provide constraints on the tidal charge parameter, which in turn will enable us to provide a possible bound on the size of the extra dimension.