Probing Quantum Gravity effects with Extreme Mass Ratio Inspirals around Rotating Hayward Black Holes

TL;DR

The paper investigates EMRIs around rotating Hayward black holes to test quantum gravity via a non-GR parameter $α_0$ that modifies orbital frequencies and GW fluxes. It derives the rotating Hayward metric, computes quantum-corrected geodesics and fluxes, and generates EMRI waveforms with the augmented analytic kludge (AAK) using the FEW package, incorporating time-delay interferometry (TDI) to suppress laser noise. A Fisher-information analysis on TDI-formed data indicates that LISA could detect dephasing and constrain $α_0$ to about $3.07\times10^{-4}$ for favorable SNRs, highlighting EMRIs as powerful probes of quantum-gravity imprints in strong-field gravity. The work emphasizes the potential of space-based GW observatories to test fundamental physics and motivates extending waveform modeling to higher-order self-force effects beyond the 0PA order.

Abstract

We investigate extreme mass-ratio inspirals (EMRIs) around a rotating Hayward black hole to assess the detectability of signatures arising from quantum gravity.The quantum parameter $α_0$, which encodes deviations from general relativity (GR), introduces extra correction terms in both the orbital frequency and the fluxes. Our results show that after one year of accumulated observation, these corrections induce a detectable dephasing in the EMRI waveform. Using the modified orbital evolution driven by $α_0$, we generate waveforms via the augmented analytic kludge (AAK) model implemented in the \texttt{FastEMRIWaveforms} package. Furthermore, we utilize the time-delay interferometry (TDI) to suppress the laser noise and phase fluctuations induced by spacecraft motion, and then employ the Fisher information matrix (FIM) to test the sensitivity of LISA in detecting deviations from GR. Our results demonstrate the potential of LISA to probe quantum-gravity effects through high-precision observations of EMRIs.

Figures (4)

• Figure 1: The phase diagram of the rotating HBH over $\{a/M, \alpha_0/M^2\}$. The blue line represents the case of extremal black hole.
• Figure 2: The orbital dephasing $\Delta \Psi$ as a function of $\alpha_0$ for different values of $a$. The gray dashed line corresponds to the LISA detection threshold of $\Delta \Psi\sim 1$ rad.
• Figure 3: The comparison of the plus polarization $h_+$ in the AAK waveform across different values of $\alpha_0$.
• Figure 4: The posterior probability distributions for the intrinsic parameters for the channels of $A,E$. The plots along the diagonal show the marginalized distribution for each individual parameter, with vertical lines marking the $1\sigma$ credible interval. The two-dimensional contours represent the $68\%$, $95\%$, and $99\%$ joint credible intervals for parameter pairs.