Black hole binaries in shift-symmetric Einstein-scalar-Gauss-Bonnet gravity experience a slower merger phase

TL;DR

The study investigates shift-symmetric Einstein-scalar-Gauss-Bonnet gravity (EsGB) for binary black holes using two independent NR formulations, revealing a surprising late-inspiral slowdown relative to general relativity due to changes in conservative dynamics, despite the expectation of faster mergers from scalar radiation alone. By aligning quasi-circular, GW150914-like waveforms and analyzing energy fluxes, they show that more energy must be emitted to increase orbital frequency in EsGB, producing a slower merger as merger approaches. Post-Newtonian theory up to $2PN$ disagrees with the NR results, highlighting the insufficiency of perturbative approaches near merger and the importance of non-linear metric backreaction. The cross-code validation and careful treatment of initial data underscore the need to revisit PN-based constraints and to perform long, non-linear simulations to accurately capture strong-field deviations in modified gravity theories. These findings suggest distinctive observational signatures in the inspiral–merger transition that could inform future gravitational-wave constraints on EsGB and related EFTs.

Abstract

In shift-symmetric Einstein-scalar-Gauss-Bonnet gravity, stationary black holes have a non-vanishing scalar charge. During the inspiral, the phase evolution is modified by several effects, primarily an additional scalar dipole radiation, which enters at -1PN order. This effect accelerates the inspiral when compared to general relativity, when including corrections up to 2PN. Using fully non-linear numerical simulations of quasi-circular, comparable mass binaries, we find that in the late stages the orbital dynamics are altered so that the overall effect is instead a decelerated merger phase for the modified gravity case. We attribute this to a change in the conservative dynamics, and show that at the late inspiral stage more energy must be emitted in scalar-Gauss-Bonnet gravity to induce a given change in frequency. In longer signals, this should lead to a distinctive switch between a faster and slower frequency evolution relative to general relativity as the binary approaches merger. This work suggests we should revisit existing constraints on the theory that are obtained assuming PN approximations apply up to merger, or based on order by order approximations that neglect backreaction effects on the metric, and shows the importance of including non-linear effects that modify the gravitational sector in the strong field regime.

Figures (9)

• Figure 1: Here we show the strain waveform for EsGB and GR for the intrinsic parameters of a GW150914-like event using the mCCZ4 formulation. The signals have been aligned in frequency and phase according to \ref{['eq:align_freq_1']}-\ref{['eq:align_freq_2']} over time window ranging from $t_i=200M$ to $t_f=600M$, the latter shown by the vertical dotted line. One can see that the GR waveform merges earlier than the EsGB case, contrary to the naive expectation that the extra scalar radiation channel will result in a faster merger. The bottom panel shows the dephasing as a function of retarded time $t_*\equiv(t-r_*)/M$.
• Figure 2: In this figure we show the phase evolution versus frequency, using the same alignment as Fig. 1. In the top panel we show the phase $\Phi$ versus frequency $f$ between GR and EsGB for the mCCZ4 code, and in the second for the MGH code. In the final panel only the difference to GR is plotted for both codes, which is the most robust comparison. Whilst the effect is small, the two show a clear consistency in predicting a slower inspiral in EsGB after alignment (seen here as more cycles accumulating in EsGB for a given change in frequency).
• Figure 3: We plot the GW $P_{\rm GW} = dE_{\rm GW}/dt$ and scalar $P_{\rm SF}$ luminosity versus frequency. We see that the GW radiation appears to be roughly consistent between GR and EsGB at a given frequency, while the scalar radiation is orders of magnitude smaller. However, in the second panel we plot the integrated GW luminosity vs the frequency and find that in the approach to merger this is smaller in GR than in EsGB, implying a modification in the binding energy at a given frequency, which is what leads to the delayed merger. In the bottom panel we plot the integrated GW luminosity versus retarded time for EsGB and GR. It can be seen that the end value is smaller for GR - less emission was needed to reach merger than in EsGB.
• Figure 4: Comparison plot for dephasing of waveforms after alignment in frequency and time. We show the dephasing between the two formulations for GR and EsGB individually, $|\Phi_{\rm GR/GB,MGH}-\Phi_{\rm GR/GB,mCCZ4}|$. We show dephasing between GR and EsGB for each formulation individually, $|\Phi_{\rm GB}-\Phi_{\rm GR}|_{\rm MGH/mCCZ4}$.We also show difference in dephasing between GR and EsGB waveform between the different formulations, $|\Delta \Phi_{\rm MGH}-\Delta \Phi_{\rm mCCZ4}|$. This shows that even though the differences between the GR/GB phases between formulations is of the same order as the magnitude of the dephasing between EsGB and GR waveform we see in each formulation, the dephasing between GR and EsGB across codes agrees very well. The green solid and blue dashed lines are the same as those shown in Fig. \ref{['fig:Phase']} of the main text.
• Figure 5: Sensitivity of results on the way we perform alignment. Dephasing between GR and EsGB waveforms for each formulation after aligning the waveforms. The subscript $f$ refers to alignment according to \ref{['eq:align_freq_1']}-\ref{['eq:align_freq_2']}, while subscript $\Phi$ to alignment performed using \ref{['eq:align_phase']}. Note that the curves with subscript $f$ are identical to the ones in the bottom panel of Fig. \ref{['fig:Phase']}. We find that the results do not depend strongly on whether we align in phase only or in frequency then phase. This figure also shows agreement between the two different formulations.