Imprints of quantum gravity effects on gravitational waves: a comparative study using extreme mass-ratio inspirals

TL;DR

This work tests quantum-gravity imprints on strong-field spacetimes by analyzing EMRIs around two covariant loop quantum gravity black hole solutions, parameterized by the deformation $\zeta$. Using an FEW-based improved AAK waveform, the authors quantify how $\zeta$ alters geodesics, orbital frequencies, and GW dephasing, and they assess detectability with the LISA detector via faithfulness analyses. They find that the type-I LQG-BH spacetime produces notably larger dephasings than the type-II case, enabling constraints on $\zeta$ down to about $10^{-3}$ for BH-I and $10^{-2}$ for BH-II with a typical EMRI in a one-year observation at $\rho=30$. These results establish EMRIs as powerful probes of Planck-scale quantum gravity effects, offering complementary bounds to those from BH shadows or stellar orbits, while highlighting the need for higher-PN or full numerical waveform refinements for precise quantification.

Abstract

Within a generally covariant Hamiltonian framework of loop quantum gravity (LQG), two black hole models parameterized by a quantum correction $ζ$ have recently been constructed. Using extreme mass-ratio inspirals (EMRIs) as high-precision probes, we investigate the imprints of this LQG deformation in the surrounding spacetime. Waveforms generated via an improved augmented analytic kludge (AAK) model in both LQG-BH backgrounds and in Schwarzschild spacetime are compared through a faithfulness analysis. This allows us to quantify the detectability of the deviation with LISA and to derive constraints on $ζ$ based on a detection threshold. We find that the first LQG-BH model produces significantly stronger signatures in EMRI signals than the second, making its quantum gravity effects more accessible to future space-borne gravitational-wave detection.

Figures (8)

• Figure 1: Relation between $K_{\mathrm{LQG-II}}$ and the LQG parameter $\zeta$ at the bounce radius $r_{\mathrm{b}}$ in the second type LQG black hole background. The parameter $\zeta$ is varied within the range $\left[0, 0.5\right]$.
• Figure 2: Deviation in the time evolution of the semi-latus rectum $\Delta p=p_{\mathrm{I, II}}-p_{\mathrm{Sch}}$ for different values of the quantum gravity parameter $\zeta$. The first row corresponds to the LQG-BH I background, and the second row to the LQG-BH II background. The left column shows results for the initial eccentricity $e_0=0.01$, and the right column for $e_0=0.1$. The initial semi-latus rectum is set to $p_0=10$ in all cases.
• Figure 3: Deviation in the time evolution of the eccentricity $\Delta e=e_{\mathrm{I, II}}-e_{\mathrm{Sch}}$ for different values of the quantum gravity parameter $\zeta$. The first row corresponds to the LQG-BH I background, and the second row to the LQG-BH II background. The left column shows results for the initial eccentricity $e_0=0.01$, and the right column for $e_0=0.1$. The initial semi-latus rectum is set to $p_0=10$ in all cases.
• Figure 4: EMRI orbital dephasing $\left | \Delta \Phi \right | =\left |{\Phi_{\phi}}_\mathrm{I, II}- {\Phi_{\phi}}_{\mathrm{Sch}}\right |$ versus evolution time for different values of $\zeta$, where the inset presents enlarged views for $\zeta=1/1000$ and $\zeta = 1/100$. The first row corresponds to the LQG-BH I background, and the second row to the LQG-BH II background. The left column shows results for the initial eccentricity $e_0=0.01$, and the right column for $e_0=0.1$. The fixed initial parameters $\left\{M, m, p_0, {\Phi_{\phi}}_0, {\Phi_{r}}_0\right\}$ are set to $\left\{10^{6} M_{\odot}, 10 M_{\odot}, 10, 0, 0\right\}$ correspondingly.
• Figure 5: Time evolution of the dephasing $\Delta \Phi={\Phi_{\phi}}_\mathrm{I, II}- {\Phi_{\phi}}_{\mathrm{Sch}}$ for various initial eccentricities at a fixed quantum gravity value of $\zeta=1/100$, where the inset shows an enlarged view around one year of orbital evolution. The left panel corresponds to the LQG-BH I background, and the right panel to the LQG-BH II background. The initial parameters $\left\{M, m, p_0, {\Phi_{\phi}}_0, {\Phi_{r}}_0\right\}$ are set to $\left\{10^{6} M_{\odot}, 10 M_{\odot}, 10, 0, 0\right\}$ correspondingly.