Assessing EMRI Detectability of the Rotating Quantum Oppenheimer-Snyder Black Hole

This letter presents an assessment of quantum gravity effects on extreme-mass-ratio inspirals (EMRIs) for the rotating quantum Oppenheimer-Snyder (qOS) black hole. Employing the adiabatic evolution, we compute the gravitational wave (GW) dephasing, which quantifies the cumulative phase shift induced by the quantum correction {\alpha} . We further generate the augmented analytic kludge (AAK) waveform and investigate the faithfulness between the waveforms with and without the quantum parameter {\alpha} for different values of a. Our results reveal that the quantum gravity effect induces detectable imprints in LISA, while the presence of rotation suppresses these signatures. This suggests that rotational degrees of freedom must be carefully accounted for when probing quantum gravity with EMRI observations.