Can we probe Planckian corrections at the horizon scale with gravitational waves?

TL;DR

Future gravitational wave detectors might distinguish black holes from exotic objects, but quantum gravity imposes a fundamental resolution limit preventing probing Planckian corrections at the horizon scale.

Contribution

This paper analyzes the potential and limitations of using gravitational waves as a microscope to probe quantum-scale corrections at black hole horizons.

Findings

Error in distance resolution is exponentially sensitive to Love number errors.

Quantum gravity's uncertainty principle sets a fundamental resolution limit.

The microscope's resolution is well above the Planckian scale.

Abstract

Future detectors could be used as a gravitational microscope to probe the horizon structure of merging black holes with gravitational waves. But can this microscope probe the quantum regime? We study this interesting question and find that (i) the error in the distance resolution is exponentially sensitive to errors in the Love number, and (ii) the uncertainty principle of quantum gravity forces a fundamental resolution limit. Thus, although the gravitational microscope can distinguish between black holes and other exotic objects, it is resolution limited well above the Planckian scale.