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

In the context of higher dimensional braneworld scenario, we have argued that the occurrence of horizonless exotic compact objects, as an alternative to classical black holes, are more natural. These exotic compact objects carry a distinctive signature of the higher dimension, namely a tidal charge parameter, inherited from the projection of the higher dimensional Weyl tensor onto the four dimensional spacetime we live in. Due to the absence of any horizon, rotating exotic compact objects are often unstable because of superradiance. Interestingly, these higher dimensional exotic compact objects, in the presence of the tidal charge, are more stable than their four dimensional counterpart. A similar inference is drawn by analysing 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 post-merger ringdown phase of the exotic compact object in the braneworld scenario, which can be described in terms of the quasi-normal modes, holds plethora of information regarding the nature of the higher dimension. In this connection we have discussed the analytical computation of the quasi-normal 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 depends 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 length of the extra dimension.