Probing Planckian Corrections at the Horizon Scale with LISA Binaries

Several quantum-gravity models of compact objects predict microscopic or even Planckian corrections at the horizon scale. We explore the possibility of measuring two model-independent, smoking-gun effects of these corrections in the gravitational waveform of a compact binary, namely, the absence of tidal heating and the presence of tidal deformability. For events detectable by the future space-based interferometer LISA, we show that the effect of tidal heating dominates and allows one to constrain putative corrections down to the Planck scale. The measurement of the tidal Love numbers with LISA is more challenging but, in optimistic scenarios, it allows us to constrain the compactness of a supermassive exotic compact object down to the Planck scale. Our analysis suggests that highly spinning, supermassive binaries at 1–20 Gpc provide unparalleled tests of quantum-gravity effects at the horizon scale.

Figure 1

TLN of ECOs [21] as a function of the distance $\delta =r_0-2M$ between the surface and the Schwarzschild radius, for an ECO mass $M={10}^6{M}_{\odot }$. From left to right, vertical strips mark different scales: Planck, subnuclear (Fermi), and microscopic scales, respectively. The horizontal bands correspond to the measurement of TLNs at the level of $k\approx 0.02$ (as routinely achievable by LISA; see Fig. 2 below) and $k\approx 0.005$ (achievable only in optimistic scenarios).

Figure 2

Percentage relative errors on the tidal-heating parameter $\gamma$ (left panel) and on the average tidal deformability $\mathrm{\Lambda }$ (right panel), as a function of the spin parameter ${\chi }_1={\chi }_2$, for different values of the mass $m_1=({10}^6,5\times {10}^6,{10}^7)M_{\odot }$. In the left panel we consider a BH binary; i.e., we assume $\gamma =1$ and $\mathrm{\Lambda }=0$, whereas in the right panel we assume an ECO binary (i.e., $\gamma =0$ and $\mathrm{\Lambda }\ne 0$, with $k=0.02$ for both binary components). Full (empty) markers refer to the mass ratio $q=1.1$ ($q=2$). Points below the horizontal line correspond to detections that can distinguish between a BH and an ECO at better than the $1\sigma$ level. We assume binaries at the luminosity distance 2 Gpc; ${\sigma }_{\mathrm{\Lambda },\gamma }$ scales with the inverse luminosity distance, whereas ${\sigma }_{\mathrm{\Lambda }}$ (${\sigma }_{\gamma }$) scales with $1/\mathrm{\Lambda }$ ($1/\gamma$) when $k\ll 1$ ($\gamma \ll 1$).