Theoretical Physics Implications of the Binary Black-Hole Mergers GW150914 and GW151226

TL;DR

The paper tackles testing General Relativity in the strong-field, dynamical regime by analyzing GW150914 and GW151226 with ppE and gIMR waveform formalisms. It translates absence of anomalies in the data into constraints on a broad set of non-GR generation and propagation mechanisms, linking them to concrete theory parameters. It also explores implications for exotic spacetimes and potential electromagnetic counterparts, illustrating both the power and limits of current models in ruling out beyond-GR physics. The findings highlight that while GR remains robust in extreme gravity, future higher-SNR and multi-band observations will be essential to fully probe non-GR effects, especially during the merger and in non-vacuum scenarios.

Abstract

The gravitational wave observations GW150914 and GW151226 by Advanced LIGO provide the first opportunity to learn about physics in the extreme gravity environment of coalescing binary black holes. The LIGO Scientific Collaboration and the Virgo Collaboration have verified that this observation is consistent with General Relativity. This paper expands their analysis to a larger class of anomalies, highlighting the inferences that can be drawn on non-standard theoretical physics mechanisms. We find that these events constrain a plethora of mechanisms associated with the generation and propagation of gravitational waves, including the activation of scalar fields, gravitational leakage into large extra dimensions, the variability of Newton's constant, a modified dispersion relation, gravitational Lorentz violation and the strong equivalence principle. Though other observations limit many of these mechanisms already, GW150914 and GW151226 are unique in that they are direct probes of dynamical strong-field gravity and of gravitational wave propagation. We also show that GW150914 constrains inferred properties of exotic compact object alternatives to Kerr black holes. We argue, however, that the true potential for GW150914 to both rule out exotic objects and constrain physics beyond General Relativity is severely limited by the lack of understanding of the merger regime in almost all relevant modified gravity theories. This event thus significantly raises the bar that these theories have to pass, both in terms of having a sound theoretical underpinning, and being able to solve the equations of motion for binary merger events. We conclude with a discussion of the additional inferences that can be drawn if the lower-confidence observation of an electromagnetic counterpart to GW150914 holds true; this would provide dramatic constraints on the speed of gravity and gravitational Lorentz violation.

Figures (15)

• Figure 1: (Color online) (Left) Third-order PN estimates of the orbital separation (top) and velocity (bottom) as a function of the GW frequency (see also Fig. 2 of Abbott:2016blz). (Right) An estimate of the square root of the spectral noise density curve of aLIGO when GW150914 was detected (as interpolated from the data made publicly available by the LVC noise-data as described in Appendix \ref{['app:noise-fit']}), and two models (PhenomB Ajith:2009bn and PhenomD Husa:2015iqaKhan:2015jqa) of the amplitude of the GW Fourier spectrum of GW150914 (GW151226) multiplied by twice the square root of the frequency, and scaled to SNR 24 (13).
• Figure 2: (Color online) Schematic diagram of the curvature-potential phase space sampled by various experiments that test GR. The vertical axis shows the inverse of the characteristic curvature length scale, while the horizontal axis shows the characteristic gravitational potential, based on Table \ref{['table:mass-length']}. GW150914 and GW151226 sample a regime where the curvature and the potential are both simultaneously large and dynamical, indicated here by the finite range the curves sweep in the figure. The finite area of pulsar timing arrays is due to the range in the GW frequency and the total mass of supermassive BH binaries that such arrays may detect in the future. Figure \ref{['fig:phase-diagram-new-time-scale']} is a companion plot that illustrates the dynamical aspects of gravity probed by these experiments; the lighter (blue) dots here are to indicate that the Shapiro time delay from binary pulsars and the Cassini satellite do not give information on the dynamical regime.
• Figure 3: (Color online) (Left) Schematic diagram of the curvature-radiation reaction time-scale phase space sampled by relevant experiments shown in Fig. \ref{['fig:phase-diagram-new']}. As is evident, GW150914 and GW151226 sample a regime of dynamic gravity where the radiation-reaction timescale is the shortest by many orders of magnitude. (Right) Characteristic curvature and strength of the Newtonian gravitational potential as a function of GW frequency.
• Figure 4: (Color online) 90%-confidence constraints on the ppE parameter $|\beta|$ at $n$th PN order. The green crosses represent the bounds reported in TheLIGOScientific:2016peaTheLIGOScientific:2016src through a Bayesian analysis of event GW150914, mapped to constraints on $\beta$. The red (magenta) dots and line represent bounds from GW150914 (GW151226) estimated with a Fisher analysis, using the IMRPhenom waveform (without spin precession) and a fit to the aLIGO spectral noise density. The constraints obtained with a Fisher analysis agree very well with the Bayesian constraint reported in TheLIGOScientific:2016peaTheLIGOScientific:2016src. The blue dotted line shows projected constraints predicted in 2011 by cornish-PPE for a system similar to GW151226. The dashed black line is a rough estimate on the constraints that the double binary pulsar PSR J0737-3039 burgaylynekramer-double-pulsar can place on the ppE $\beta$ parameter Yunes:2010qb, while the cyan star refers to the bound on $\beta$ at 1PN from the perihelion precession of Mercury Sampson:2013wia. Binary pulsar observations can constrain negative PN order deviations better than aLIGO, while aLIGO does better than binary pulsar observations at higher PN order, as first calculated in Yunes:2010qb. However, note also that binary pulsar and Solar System bounds cannot be directly compared to GW ones as the binary pulsar (Solar System) one corresponds to the extreme case of no conservative (no dissipative) corrections. Moreover, stronger constraints on $\beta$ for these latter tests do not necessarily mean stronger constraints on modifications to GR for BH mergers, as $\beta$ depends not only on theoretical coupling parameters but also on system parameters, and in certain theories (like EdGB gravity), non-GR corrections are suppressed in stars compared to BHs.
• Figure 5: (Color online) Upper bound on corrections to the binding energy $|A|$, energy flux $|B|$ [see Eq. \ref{['eq:binding-energy-flux']}] and a combination of these two $|C|$ [see Eq. \ref{['eq:beta-ABC']}] as a function of the PN order that they enter for GW150914 (red) and GW151226 (blue).