Black Hole Binary Dynamics from the Double Copy and Effective Theory (1908.01493v2)

Abstract: We describe a systematic framework for computing the conservative potential of a compact binary system using modern tools from scattering amplitudes and effective field theory. Our approach combines methods for integration and matching adapted from effective field theory, generalized unitarity, and the double-copy construction, which relates gravity integrands to simpler gauge-theory expressions. With these methods we derive the third post-Minkowskian correction to the conservative two-body Hamiltonian for spinless black holes. We describe in some detail various checks of our integration methods and the resulting Hamiltonian.

• The paper introduces a 3PM correction to the two-body Hamiltonian for spinless black holes using double copy and unitarity to extract classical potential contributions.
• It applies classical truncation and effective field theory matching to disentangle quantum artifacts and derive precise gravitational interaction terms.
• The study advances gravitational wave modeling by refining waveform templates through higher-order corrections in black hole binary dynamics.

Overview of the Paper: Black Hole Binary Dynamics from the Double Copy and Effective Theory

The paper focuses on developing a systematic framework for understanding the dynamics of black hole binary systems, leveraging the modern advancements in scattering amplitudes and effective field theory (EFT). This approach is designed to yield the conservative potential of compact binary systems within the post-Minkowskian (PM) framework. Specifically, the paper provides the third PM correction to the two-body Hamiltonian for spinless black holes, a regime of relevance for gravitational wave astronomy, as it aligns with the sensitivity improvements anticipated in next-generation detectors.

Key Contributions and Methods

1. Double Copy Construction and Generalized Unitarity: The paper employs the double-copy formalism combined with generalized unitarity methods. This dual approach allows the authors to express complex gravitational interactions in terms of simpler gauge theory amplitudes. The double copy relates gravitational processes to gauge theories, harnessing the simpler perturbative expansions available in gauge theory calculations.
2. Treatment of Integrands in Classical Physics: One decisive contribution is the application of classical truncation principles to obtain integrands efficiently. Only particular unitarity cuts that preserve classical potential contributions are considered, dropping quantum mechanical iterations that contribute no new classical dynamics.
3. Effective Field Theory Matching: Another significant result is derived from matching the computed PM amplitude to its EFT analog. This procedure systematically disentangles iteration terms, leading to the explicit formulation of the 3PM conservative potential. The techniques trace the behavior of scattering amplitudes dominated by potential modes, leading to accurate extraction of classical contributions without succumbing to quantum artifacts.
4. Singularity Discoveries and Regularization: The work uncovers a mass singularity in the 3PM potential—a logarithmic divergence that fails to smooth out as massless limits are considered. Unlike similar studies of massless scattering, this divergence epitomizes the intricacies faced when tracking classical limits across differing gravitation regimes.

Results and Numerical Findings

The paper presents several numerical results showcasing the potential contributions at the 1PM, 2PM, and 3PM levels. The derived potential stands conformant with previously published results within its lower-order dynamic range, ensuring a trustworthy integration across different theoretical domains, such as the 4PN framework.

Theoretical and Practical Implications

Practically, refining gravitational wave templates lies at the core of these developments. The conservative dynamics characterized in this paper are indispensable to the synthesis of waveform models that gravitational detectors require. Theoretically, this research strengthens the interplay between gauge theories and gravity, producing streamlined calculations that benefit from gauge-theory perturbative advantages.

Future Developments

Further directions may involve extending these findings to spinning black holes or including tidal effects within the scope of EFT applications. Incorporating radiation reaction effects, which become relevant beyond the current 3PM scope, may also introduce new sets of challenges and necessitate novel methodological approaches.

Overall, the paper deftly integrates modern theoretical frameworks to bridge classical gravitational dynamics with quantum amplitude methodologies, offering a pivotal advancement in theoretical astrophysics. By achieving higher-order precision in potential calculations, it sets a promising frontier for future investigations into the complexities of binary black hole interactions.