Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory (2005.03071v1)

Abstract: We describe a systematic framework for finding the conservative potential of compact binary systems with spin based on scattering amplitudes of particles of arbitrary spin and effective field theory. An arbitrary-spin formalism is generally required in the classical limit. By matching the tree and one-loop amplitudes of four spinning particles with those of a suitably-chosen effective field theory, we obtain the spin1-spin2 terms of a two-body effective Hamiltonian through O(G^2) and valid to all orders in velocity. Solving Hamilton's equations yields the impulse and spin changes of the individual bodies. We write them in a surprisingly compact form as appropriate derivatives of the eikonal phase obtained from the amplitude. It seems likely this structure persists to higher orders. We also point out various double-copy relations for general spin.

Overview of Spinning Black Hole Binary Dynamics, Scattering Amplitudes, and Effective Field Theory

This paper presents a comprehensive framework for studying the dynamics of spinning black hole binaries using scattering amplitudes and effective field theory (EFT). The authors offer a method to derive the conservative potential of compact spinning binary systems through systematic exploration of tree and one-loop amplitudes in the context of quantum field theories.

The paper begins by establishing the importance of gravitational wave observations and the need for theoretical tools that match this precision. Various approaches like numerical relativity and post-Newtonian (PN) approximations are mentioned; however, emphasis is placed on post-Minkowskian (PM) expansions, which are relativistic weak-field expansions dependent on Newton's constant.

The authors employ the sophisticated method of scattering amplitudes to derive the necessary components of classical interactions and incorporate them into a unified EFT framework. By focusing on gauge-invariant quantities, the paper implies ease in verifying results and importing them into gravitational-wave models. The formalism offers accuracies to $\mathcal{O}(G^2)$ through all orders in velocity, aiding precision gravitational-wave predictions involving spinning binary systems such as Kerr black holes or neutron stars.

Key Findings:

1. Classical Limit of Scattering Amplitudes: The paper explores the classical limit of quantum scattering amplitudes, taking the large-spin limit of higher-spin fields to ensure all relevant classical interactions are captured. This is pivotal to incorporate spin dynamics into gravitational interactions.
2. Tree-Level and One-Loop Amplitudes: The paper provides explicit constructions of tree-level and one-loop amplitudes for spinning particles. This formulation allows verification against existing amplitudes and serves as building blocks for the derived potential.
3. Effective Field Theory (EFT) Construction: The constructed EFT for spinning objects is the backbone of the paper's method to translate quantum scattering amplitudes into classical Hamiltonians. This translation is crucial for studying bound-state problems and extracting physical observables from classical dynamics.
4. Two-Spinning-Body Hamiltonian: Focusing particularly on interactions linear in each body's spin — termed spin$_1$-spin$_2$ — the authors present a Hamiltonian valid through order $G^2$. This contribution is new and extends known results at various PN levels.
5. Relation to Eikonal Phase: The solution for observables like momentum transfer and spin changes is related to the eikonal phase derived from amplitude construction. This integration highlights deeper connections between quantum amplitudes and classical physics.

Implications and Future Directions

The introduction of arbitrary spins through higher-spin fields, combined with EFT, may lead to new precision tools in gravitational physics beyond the PN frame. The paper's methodologies could be valuable for further exploration of Kerr black holes with non-negligible spin multipole moments, potentially adding new insights into neutron star dynamics and other astrophysical bodies.

Future work should focus on extending these setups to high orders in spin and Newton coefficients, exploring gravitational interactions' quantum roots more closely, and validating this approach across the observational domain.

Overall, this paper offers a detailed analysis using scattering amplitudes and effective field theory, suggesting hidden simplicity in gravitational observables and feeding into the search for streamlined theoretical processes, potentially impacting the broader arena of quantum field theory and astrophysical dynamics.