Transient electromagnetic sources can detect solitary black holes in Milky Way galaxy

The Milky Way galaxy is estimated to host up to a billion stellar-mass solitary black holes (BHs). The number and distribution of BH masses can provide crucial information about the processes involved in BH formation, the existence of primordial BHs, and the interpretation of gravitational wave (GW) signals detected in LIGO-VIRGO-KAGRA. {Sahu et al. recently confirmed one solitary stellar-mass BH in our galaxy using astrometric microlensing}. This work proposes a novel mechanism to identify such BH by analyzing the frequency and damping of the quasi-normal modes of GW generated from the interaction of the BH and EM wave originating from a transient electromagnetic (TEM) source. The incoming EM waves distort the curvature of a BH, releasing GWs as it returns to a steady state. Using the covariant semi-tetrad formalism, we quantify the generated GWs via the \emph{Regge-Wheeler tensor} and relate the GW amplitude to the energy of the TEM. We demonstrate that isolated BHs at a distance of 50 pc from Earth can be detected by LIGO A+ and 100 pc by Cosmic Explorer/Einstein Telescope. Additionally, we discuss the observational implications for orphan afterglows associated with GRBs, highlighting the potential for further discoveries.