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Several quantum-gravity models of compact objects predict microscopic or evenPlanckian corrections at the horizon scale. We explore the possibility ofmeasuring two model-independent, smoking-gun effects of these corrections inthe gravitational waveform of a compact binary, namely the absence of tidalheating and the presence of tidal deformability. For events detectable by thefuture space-based interferometer LISA, we show that the effect of tidalheating dominates and allows one to constrain putative corrections down to thePlanck scale. The measurement of the tidal Love numbers with LISA is morechallenging but, in optimistic scenarios, it allows to constrain thecompactness of a supermassive exotic compact object down to the Planck scale.Our analysis suggests that highly-spinning, supermassive binaries at 1-20 Gpcprovide unparalleled tests of quantum-gravity effects at the horizon scale.

Probing Planckian corrections at the horizon scale with LISA binaries