Probing charge of compact objects with gravitational microlensing of gravitational waves

Gravitational microlensing of gravitational waves (GWs) opens up the exciting possibility of studying the spacetime geometry around the lens. In this work, we investigate the prospects of constraining the `charged' hair of a charged gravitating object from the observation of a GW signal microlensed by the same. The charge can have electromagnetic or modified gravity origin. We compute the analytic form of the lensing potential with charge and construct the lensed waveforms for a range of mass and charge of the charged object, assuming them to be non spinning. Using an approximate likelihood function, we explore how future observations of microlensed GWs can constrain the charge of the lens. We conclude that lensing observations are unlikely to be able to constrain the electromagnetic charge of black holes. However, we might be able to put modest constraints on certain modified gravity models (e.g., the brandworld scenario) or the possibility of the lenses being exotic objects (e.g., naked singularities) .