Quantum Love numbers

The response of a gravitating object to an external tidal field is encoded in its Love numbers, which identically vanish for classical black holes (BHs). Here we show, using standard time-independent quantum perturbation theory, that for a quantum BH, generically, the Love numbers are nonvanishing and negative, and that their magnitude depends on the lowest-lying levels of the quantum spectrum of the BH. We calculate the quadrupolar electric quantum Love number of slowly rotating BHs and show that it depends most strongly on the first excited level of the quantum BH. We then compare our results to the same Love number of exotic ultra compact objects and to that of classical compact stars and highlight their different parametric dependence. Finally, we discuss the detectability of the quadrupolar quantum Love number in future precision gravitational-wave observations and show that, under favorable circumstances, its magnitude is large enough to imprint an observable signature on the gravitational waves emitted during the inspiral phase of two moderately spinning BHs.

Automated summary

This study investigates the Love numbers of quantum black holes and finds that they are generally nonvanishing and negative, with magnitude dependent on the energy levels of the black holes. By comparing the Love numbers of exotic ultra compact objects and classical compact stars, it is shown that they have different parametric dependence. The detectability of the quadrupolar quantum Love number in future precision gravitational-wave observations is discussed and it is demonstrated that, under certain conditions, its magnitude is large enough to leave an observable signature on the gravitational waves emitted during the inspiral phase of moderately spinning black holes.