Loop Quantum Gravitational Signatures via Love Numbers

TL;DR

This paper investigates how loop quantum gravity modifies black hole properties, showing non-zero, negative Love numbers that could serve as observable quantum signatures distinguishing quantum black holes from classical ones.

Contribution

It demonstrates that loop quantum effects induce measurable tidal Love numbers in black holes, providing a potential observational window into quantum gravity.

Findings

Loop quantum black holes have non-zero, negative Love numbers.

Love numbers decrease with increasing black hole mass.

Quantum effects produce detectable 'quantum hair' in black holes.

Abstract

Loop quantum gravitational effects can resolve the central singularity of black holes while potentially leaving tiny traces of quantization in the exterior spacetime. We show the way these residues can, in principle, be explored using tidal Love numbers (TLNs). We consider loop quantized Schwarzschild black hole, in particular the Ashtekar-Olmedo-Singh (AOS) model, and study the static response to external tidal fields of spin zero (scalar field), spin one (vector field), and spin two (axial gravitational field) types. We find that, in contrast to the classical theory, where TLNs vanish, they are non-vanishing and negative for all three responses and for all multipoles. Besides, the magnitude of TLNs decreases as the black hole mass increases, and TLNs, in response to the axial gravitational field, have the largest magnitude among these three responses. Our results show that for black holes of mass $M \gtrsim 4.3 \times 10^{4} M_{\textrm{Pl}}$, the AOS model is consistent with current and next-generation detection limits for TLNs. Our findings suggest that the quantum deformability of loop quantum black holes, arising from the inherent fuzziness of spacetime geometry, reveals a fundamentally distinct internal structure compared to their classical counterparts. This unique feature manifests as quantum hair, which, in principle, can be detected by future observations.