Inspiral-Transition-Plunge Gravitational Waveforms Beyond Kerr: A Kerr-Newman Case Study

TL;DR

This work develops inspiral–transition–plunge gravitational waveforms for binaries with a Kerr–Newman primary by employing the Dudley–Finley approximation to decouple perturbations and a Teukolsky-like framework to compute GW emission from equatorial circular orbits. It constructs a continuous worldline that stitches together the adiabatic inspiral, a transition near ISCO, and a plunge, then produces full ITP waveforms and analyzes their observational prospects. The authors show that including post-inspiral dynamics significantly tightens constraints on the BH charge for intermediate-mass-ratio mergers detectable by ET, with thresholds reaching $|Q|/M \sim$ a few $\times 10^{-3}$, and demonstrate that EMRIs could reveal even smaller charges via accumulated dephasing over multi-year observations. This establishes a groundwork for beyond-Kerr waveform modeling and motivates future extensions to fully coupled perturbations and more general orbits to probe non-Kerr signatures in forthcoming GW data.

Abstract

Binary black hole mergers with asymmetric component masses are key targets for both third-generation ground-based and future space-based gravitational-wave (GW) detectors, offering unique access to the strong-field dynamics of gravity. The evolution is commonly divided into three stages: the adiabatic inspiral, the transition, and the plunge. To date, constructions of inspiral-transition-plunge waveforms have largely focused on Schwarzschild or Kerr background spacetimes. In this paper, we extend these efforts to spacetimes beyond Kerr by constructing such waveforms in a Kerr-Newman background. For simplicity, we allow the primary black hole to carry spin and charge while keeping the secondary object neutral and non-spinning. We work in the small charge-to-mass ratio regime and adopt the Dudley-Finley approximation, in which the gravitational and electromagnetic perturbations decouple. In particular, the gravitational sector satisfies a Teukolsky-like equation, enabling only minimal modifications relative to the Kerr case when constructing the waveform. Having the inspiral-transtion-plunge waveforms in hand, we studied observational prospects for constraining the charge of the central black hole. We find that, for intermediate-mass-ratio mergers observed with the Einstein Telescope, explicitly modeling the post-inspiral dynamics significantly tightens charge-to-mass ratio constraints. In particular, the bounds on the charge-to-mass ratio can reach $O(10^{-3})$ in the region of primary masses and spins where the post-inspiral signal dominates, yielding charge bounds that can be orders of magnitude tighter than those obtained from the inspiral alone or from the current bound with GW150914. These results lay the groundwork for inspiral-transition-plunge waveform modeling in beyond-Kerr spacetimes and for probing non-Kerr signatures in future GW observations.

Figures (13)

• Figure 1: Gravitational waveforms of the $(\ell,m)=(2,2)$ mode are shown for intermediate–mass–ratio binary mergers with the mass ratio $\eta = 10^{-3}$, evaluated at an inclination angle $\iota = \pi/2$, for the BH spin $a/M = 0.5$. The black dashed curve represents the Kerr case ($Q/M = 0$), while the colored solid curves correspond to $(Q/M)^2 = 0.001$ (navy), $0.005$ (green), and $0.01$ (yellow).
• Figure 2: Distinguishable charge-to-mass ratio $|Q|^\mathrm{(thr)}/M$ using the inspiral-transition-plunge, inspiral, and post-inspiral waveforms with ET. The horizontal black dashed line indicates the threshold charge for GW150914 $|Q|/M = 0.3$Bozzola:2020mjxCarullo:2021oxn, shown for reference.
• Figure 3: Energy flux $\mathcal{F}$ for $|Q|/M=0, 0.1, 0.2, 0.3, 0.4,$ and $0.5$ with $a/M=0$. For illustration, we consider relatively large values of $|Q|$ here. The inset zoom in to the region near ISCO for each $Q/M$.
• Figure 4: Inspiral-transition-plunge trajectory on the equatorial plane for $a/M=0, Q/M=0,$ and $\eta=10^{-3}$, starting at $r=7M$. Blue, green, and red lines show the inspiral, transition, and plunge, respectively. Black solid and gray dashed lines depict the ISCO and outer horizon.
• Figure 5: Time evolution of the orbital radius $r/M$ for inspiral–transition–plunge trajectories with different values of $Q/M$ and a fixed value of $a/M=0$. Each trajectory begins at $r = 7M$. The black dashed curve corresponds to the Schwarzschild case, while the colored solid curves show the charged cases with $(Q/M)^2 = 0.001$ (navy), $0.005$ (green), and $0.01$ (yellow).