A new study explores how gravitational waves from extreme-mass-ratio inspirals (EMRIs) could reveal the geometry of charged black holes inspired by Loop Quantum Gravity (LQG). Researchers have modeled the motion of test particles and the resulting gravitational wave emission in the spacetime of these objects, where the classical singularity is replaced by a smooth transition surface, its radius determined by the LQG area gap condition. The LQG polymerization parameter $\delta_b$ is uniquely determined by the black hole's mass $M$ and charge $Q$, allowing for the study of quantum corrections in all analyzed scenarios.

The work classified periodic orbits using the Levin-Perez-Giz zoom-whirl taxonomy, which relates orbital topology to the gravitational waveform. Each closed trajectory is labeled by a triple integer $(z, w, v)$ and characterized by the rational frequency ratio $q = \omega_\varphi/\omega_r - 1$. The innermost stable circular orbits (ISCO) and marginally bound orbits (MBO) were calculated from the effective potential, providing key reference points for particle dynamics.

Using the quadrupole approximation, gravitational waveforms for EMRIs were estimated, yielding polarizations in both time and frequency domains. Time-domain polarizations exhibit a zoom-whirl morphology, with waveform amplitude and phase dependent on the LQG parameter. The characteristic strain peaks in the millihertz band for all values of the charge parameter $Q$, exceeding the projected sensitivities of detectors like LISA, Taiji, and TianQin. This suggests that future observations could place meaningful constraints on the LQG polymerization parameter in the strong-field regime.