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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. 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. Finally, we discuss the detectability of the quadrupolar quantum Love number in future precision gravitational-wave observations and show that, under favourable 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. [ABSTRACT FROM AUTHOR]

The evidence for supermassive Kerr black holes in galactic centers is strong and growing, but only the detection of gravitational waves will convincingly rule out other possibilities to explain the observations. The Kerr space–time is completely specified by the first two multipole moments: mass and angular momentum. This is usually referred to as the "no-hair theorem," but it is really a "two-hair" theorem. If general relativity is the correct theory of gravity, the most plausible alternative to a supermassive Kerr black hole is a rotating boson star. Numerical calculations indicate that the space–time of rotating boson stars is determined by the first three multipole moments ("three-hair theorem"). The Laser Interferometer Space Antenna (LISA) could accurately measure the oscillation frequencies of these supermassive objects. We propose to use these measurements to "count their hair," unambiguously determining their nature and properties. [ABSTRACT FROM AUTHOR]