Can We Probe Planckian Corrections at the Horizon Scale with Gravitational Waves?

Future detectors can be used as gravitational microscopes 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, (ii) the uncertainty principle of quantum gravity forces a fundamental resolution limit, and (iii) conclusions about the structure of spacetime at small distances rely on assumptions about the properties of the (unknown) compact objects considered.

Figure 1

Inferred values of $\delta$ and $1\sigma$ errors with [black, Eq. (7)] and without [red, Eq. (10)] quantum fluctuations. We have here assumed a GW observation of a compact ECO inspiral with $m_1=1.1\times {10}^6{M}_{\odot }$ and $m_2={10}^6{M}_{\odot }$, dimensionless spin ${\chi }_{1,2}$, and Love numbers $k_1=k_2=0.02$ at a distance of 2 Gpc. For the uncertainties in $M$ and $k$, we used ${\sigma }_M^{\mathrm{stat}}/\widehat{M}={10}^{-5}$ and ${\sigma }_k^{\mathrm{stat}}/\widehat{k}\in (0.2,1)$ (see the Supplemental Material [42]), whereas for the quantum fluctuations, we set $a=1$. Observe that the error bars on the inferred value of $\delta$ are much larger than the measurement itself.