Classical Love number for quantum black holes

We present a method for comparing the classical and quantum calculations of electric quadrupolar Love number $k_2$ show that our previous derivation blackhole matches exactly calculation when expectation values are replaced by corresponding quantities, as dictated Bohr correspondence principle. The standard relativistic stars relies on fixing boundary conditions surface star Einstein equations in presence an external perturbing field. An alternative calculating uses properties spectrum non-relativistic fluid modes star. adopt this use it to derive effective description interior terms collection driven harmonic oscillators characterized different frequencies amplitudes. compare these two methods find most information can be integrated out, reducing problem single condition perturbed deformed then determine object proceed identify relationship between quantities verify agreement results calculation.