Classical Love for Quantum Blackholes

Understand

We present a method for comparing the classical and quantum calculations of the electric quadrupolar Love number $k_2$ and show that our previous derivation of the quantum Love number of a quantum blackhole matches exactly 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 standard derivation of $k_2$ for classical relativistic stars relies on fixing boundary conditions on the surface of the star for the Einstein equations in the presence of an external perturbing field.
• An alternative method for calculating $k_2$ uses properties of the spectrum of the non-relativistic fluid modes of the star.
• We adopt this alternative method and use it to derive an effective description of the interior modes in terms of a collection of driven harmonic oscillators characterized by different frequencies and amplitudes.