Numerical binary black hole mergers in dynamical Chern-Simons: I. Scalar field

Abstract: Testing general relativity in the non-linear, dynamical, strong-field regime of gravity is one of the major goals of gravitational wave astrophysics. Performing precision tests of general relativity (GR) requires numerical inspiral, merger, and ringdown waveforms for binary black hole (BBH) systems in theories beyond GR. Currently, GR and scalar-tensor gravity are the only theories amenable to numerical simulations. In this article, we present a well-posed perturbation scheme for numerically integrating beyond-GR theories that have a continuous limit to GR. We demonstrate this scheme by simulating BBH mergers in dynamical Chern-Simons gravity (dCS), to linear order in the perturbation parameter. We present mode waveforms and energy fluxes of the dCS pseudoscalar field from our numerical simulations. We find good agreement with analytic predictions at early times, including the absence of pseudoscalar dipole radiation. We discover new phenomenology only accessible through numerics: a burst of dipole radiation during merger. We also quantify the self-consistency of the perturbation scheme. Finally, we estimate bounds that GR-consistent LIGO detections could place on the new dCS length scale, approximately $\ell \lesssim \mathcal{O}(10)~\mathrm{km}$.

• The paper numerically simulates binary black hole mergers in dynamical Chern-Simons gravity using a perturbative scheme up to $\mathcal{O}(\ell^2)$ to ensure well-posedness.
• A key finding is the detection of a novel burst of dipole radiation during the black hole merger phase, which is inaccessible through traditional post-Newtonian methods.
• The study evaluates the regime of validity for the perturbative method, providing insights into the limits of the approximation and potential for future tests with gravitational wave observations.

Analyzing Binary Black Hole Mergers in Dynamical Chern-Simons Gravity

The study under review presents a comprehensive investigation of binary black hole (BBH) systems within the framework of dynamical Chern-Simons (dCS) gravity, a modification of general relativity (GR) characterized by the inclusion of a pseudoscalar field coupled to the Pontryagin density. This work represents a significant advancement in exploring gravitational theories beyond GR, specifically targeting the strong-field, dynamical regime where GR has not been rigorously tested.

Methodology and Numerical Simulations

Employing the Spectral Einstein Code (SpEC), the authors developed a perturbation scheme to address potential issues related to the ill-posedness of the initial value problem in dCS gravity. The approach hinges on a perturbative expansion in terms of a small coupling parameter, $\ell$, which quantifies deviations from GR. This framework ensures numerical stability and the well-posedness of the formulation by perturbatively solving the field equations up to first order in $\mathcal{O}(\ell^2)$.

The simulations encompass BBH scenarios with varying dimensionless spin parameters ($\chi = 0.0, 0.1, 0.3$), focusing on aligned-spin configurations to maintain analytical tractability. By choosing equal mass ratios and spins, the study strategically aims at understanding the interaction of spin with scalar field dynamics.

Key Findings and Theoretical Implications

1. Agreement with Post-Newtonian Predictions: At early inspiral stages, the numerical results show qualitative concordance with post-Newtonian (PN) predictions. Notably, early-time scalar field configurations align well with PN calculations, where the $(l=2, m=1)$ scalar mode dominates the radiation.
2. New Phenomenology: A novel burst of dipole radiation is observed during the merger phase. This effect is inaccessible via traditional PN methods, underlining the significance of numerical relativity in uncovering non-linear, strong-field gravitational phenomena.
3. Energy Flux Analysis: The investigation of energy flux reveals that while the scalar field contribution is significantly smaller than the gravitational radiation in the inspiral phase, there is a notable increase around merger. This underscores the subtle yet impactful role of scalar fields in BBH dynamics within dCS gravity.
4. Regime of Validity: The study methodically examines the regimes of perturbative and secular validity. Instantaneous convergence conditions are articulated through an examination of the perturbative series’ behavior, yielding estimations for the permissible range of $\ell/GM$. Secular deviations, gauged through orbital phase differences, are evaluated, indicating where perturbation theory begins to drift from 'true' solutions.

Prospective Applications and Future Directions

The work accentuates the potential of BBH mergers as astrophysical laboratories for testing gravitational theories beyond GR. As Advanced LIGO and Virgo continue to observe BBH mergers, the capability to simulate such systems in non-GR contexts paves the way for direct confrontation of theoretical predictions with empirical data. Future studies could extend to $\mathcal{O}(\ell^4)$ computations, enabling direct waveform modifications that might be detectable in gravitational wave signals.

Furthermore, the perturbation framework employed here is adaptable to other modified gravity theories, such as Einstein-dilaton-Gauss-Bonnet (EdGB) theories, thus broadening the scope of verification against experimental data. This could be invaluable as gravitational wave observatories refine their detection capabilities and sensitivity.

The intricate balance between rigorous analytical calculations and computational simulations highlights the nuanced interplay of theoretical physics with observational astronomy in advancing our understanding of the fundamental principles governing our universe. The outcomes of this research have implications for fundamental physics, potentially offering insights into unresolved issues like the black hole information paradox and the limits of classical gravity theories.