Gravitational-wave signatures of non-violent non-locality

Abstract

Measurement of gravitational waves can provide precision tests of the nature of black holes and compact objects. In this work, we test Giddings' non-violent non-locality proposal, which posits that quantum information is transferred via a nonlocal interaction that generates metric perturbations around black holes. In contrast to firewalls, these quantum fluctuations would be spread out over a larger distance range -- up to a Schwarzschild radius away. In this letter, we model the modification to the gravitational waveform from non-violent non-locality. We modify the nonspinning EOBNRv2 effective one body waveform to include metric perturbations that are due to a random Gaussian process. We find that the waveform exhibits random deviations which are particularly important in the late inspiral-plunge phase. We find an optimal dephasing parameter for detecting this effect with a principal component analysis. This is particularly intriguing because it predicts random phase deviations across different gravitational wave events, providing theoretical support for hierarchical tests of general relativity. We estimate the constraint on the perturbations in non-violent non-locality with events for the LIGO-Virgo network and for a third-generation network.

Figures (9)

• Figure 1: The real part of the dimensionless $h_{22}(t)$ strain for $A_{22} = 5\times 10^{-2}$. This is the full waveform before the PCA is done, so it contains all perturbations. These signals are aligned at very early times so that their signals overlap at low frequencies but they stochastically diverge as they reach the plunge. The apparent ringdown difference is primarily due to the phenomenological ringdown attachment, but we only do the testing GR analyses with the inspiral piece.
• Figure 2: Frequency domain phase deviation realizations for $A_{22} = 1$. Using time domain waveform realizations shown in Fig. \ref{['fig:td-wf']}, we plot the amount of dephasing from GR that they will have. We also plot the frequency at which the binary crosses the inner most stable circular orbit (dashed blue) and the frequency at which the inspiral portion of the waveform is matched to the ringdown (dashed black). Note that $A_{22} = 1$ is not a small deviation from GR, so we calculated this at $A_{22} \ll 1$ and scaled it appropriately. One can see that the secular effect of NVNL is nearly zero while the theory predicts random dephasing from GR.
• Figure 3: The largest PCA modes of the covariance matrix. All modes with odd $l+m$ are zero since we are confined to the orbital plane with $\theta = \pi/2$. The largest eigenvector accounts for $\sim 97\%$ of the phase variance for each of the modes. One can see that similar deviations happen for all $(\ell, m)$ modes.
• Figure 4: The log Bayes factor projected constraint for Hanford-Livingston-Virgo network operating at O3 Livingston sensitivity (positive favors GR). We plot this for various values of $A$ and for increasing numbers of events. The line corresponding to -10 log Bayes factor is shown for the optimal PCA model (black) and PN coefficients (other colors) where GR is disfavored. Using an event list, we perform parameter estimation for five years of detectable events and then compute the Bayes factor for the hierarchical test of GR. Note that the PCA model is best able to constrain the effects of NVNL most stringently, but the PN coefficients are able to detect a violation of $A\ne0$ nearly as well. We also see that the largest PN orders perform the best. For a five year observation, the bound for the PCA model is $A < 1.6\times 10^{-2}$.
• Figure 5: The log Bayes factor for the Hanford-Livingston-Virgo network operating at CE sensitivity (positive favors GR). This plot shows the same scaling as Fig. \ref{['fig:bayes-factor-result-O3']}, but contains more events since CE detects more in a five year period. For a five year observation, the bound for the PCA model is $A < 1.2\times 10^{-3}$.