Quantum Love

Abstract

The response of a gravitating object to an external tidal field is encoded in its Love numbers, which identically vanish for classical blackholes (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 nonrotating 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 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.

Classical Love for Quantum Blackholes

“…We wish to understand the origin of the QBH classical Love number that we have just calculated. We first briefly recall our previous calculation of the quantum Love number [12] and then show that the results match exactly the results of the classical calculation of k 2 when quantum expectation values are replaced by the corresponding classical quantities, as dictated by the Bohr correspondence principle. The correspondence of the quantum to classical Love number results is not a coincident, it indicates the consistency of these two different methods and provides us with an explicit dictionary, translating quantum observables into classical GR quantities.…”

“…Following similar considerations, we derived in [12] an expression for the gravitational polarizability -the Love numbers. The derivation proceeded by replacing the electric field and the dipole moment by the tidal fields and the mass and current moments, correspondingly.…”

“…In [12] we evaluated the correction to the ground state energy due to the induced quadrupole, Q ij of a nonrotating quantum BH whose Schwarzschild radius is R S . Recall that in the classical case,…”

“…We argued in [12] that future observations by the planned Laser Interferometer Space Antenna (LISA) [13] of GW emitted during the inspiral phase of binary BHs coalescence events will provide an opportunity for probing the quantum state of macroscopic astrophysical blackholes (BHs) via the imprint of this state on the emitted GW. Our argument was based on showing that the electric quadrupolar Love number k 2 , is non-vanishing for a quantum BH (QBH) and could be, under favourable circumstances, large enough for LISA to measure (similar arguments are also given in [14]).…”

“…Moreover, it was argued that modifications to the nature of BHs of quantum origin are needed to reconcile some fundamental problems such as the information loss paradox [17,18,19]. Among the suggested quantum ultracompact objects that could be relevant in this context are, for example, Firewalls [18,20], fuzzballs [21], BH polymers [22], and many others, [12,23,24,25,26,27,28,29]. We will refer collectively to the quantum object that corresponds to a classical BH as a "quantum blackhole" (QBH).…”