Love Numbers of Covariant Loop Quantum Black Holes

TL;DR

This paper calculates the tidal Love numbers of covariant loop quantum black holes, revealing they are generally nonzero and depend on quantum model details, which could help distinguish different quantum gravity theories.

Contribution

It provides the first detailed computation of TLNs for covariant loop quantum black holes, highlighting their nonzero values and dependence on quantum model parameters.

Findings

TLNs are generally nonzero for loop quantum black holes.

TLNs depend on the spin, multipole number, and quantum model details.

TLNs are Planck scale suppressed, larger for the ABV model than ZLMY.

Abstract

We investigate the linear static response of three covariant loop quantum black holes, namely, the two models proposed by Zhang, Lewandowski, Ma, and Yang (ZLMY) and the Alonso-Bardaji, Brizuela, and Vera (ABV) model, to an external tidal field. Using effective spacetime description, we uniquely extract the tidal Love numbers (TLNs) using perturbative solutions derived from the Green's function technique. Our findings reveal that, in contrast to the classical Schwarzschild black hole, the TLNs for loop quantum black holes are generally nonzero. The sign and magnitude of the TLNs depend on the spin of the external tidal field, the multipole number, and the details of the loop quantized model. The magnitude of the TLNs is found to be Planck scale suppressed for all three models, implying a stronger tidal deformability for black holes with Planckian mass. Additionally, for the same black hole mass, the magnitude of the TLNs for the ABV model is larger than the ZLMY models. We also find that the TLNs exhibit logarithmic running behavior at the leading order, even for low multipole numbers, in response to scalar and vector field perturbations. These distinct features of the TLNs can serve as a potential tool to differentiate between various quantization ambiguities arising in loop quantum black holes. We briefly discuss the potential phenomenological and theoretical implications of nonzero TLNs for black hole physics.