Binary Dynamics through the Fifth Power of Spin at O(G^{2})

Area of Science:

• Theoretical Physics
• Gravitational Wave Astronomy
• Black Hole Physics

Background:

• Accurate modeling of binary systems, especially those involving compact objects like black holes, is essential for interpreting gravitational wave signals.
• Previous theoretical frameworks have faced challenges with unphysical singularities and higher-time derivatives when calculating two-body Hamiltonians.
• The quadratic-in-spin two-body Hamiltonian has been previously determined up to O(G^2).

Purpose of the Study:

• To extend the calculation of two-body Hamiltonians for generic binary systems with arbitrary spin (S) to higher orders.
• To introduce and evaluate new operators arising from a subtlety in the formalism.
• To confirm the validity of the extended calculations by comparing with aligned-spin results and to conjecture a method for determining Kerr black hole Wilson coefficients to all orders in spin.

Main Methods:

• Utilizing a previously developed scattering-amplitudes-based framework designed to avoid unphysical singularities and higher-time derivatives.
• Evaluating the S^3 scattering angle and two-body Hamiltonian at O(G^2), including standard worldline operators and additional operators.
• Calculating S^4 and S^5 contributions at O(G^2) and comparing results with aligned-spin calculations.

Main Results:

• The S^3 scattering angle and two-body Hamiltonian have been evaluated at O(G^2), incorporating novel operators.
• S^4 and S^5 contributions at O(G^2) have been successfully computed and validated against aligned-spin results.
• A conjecture is proposed regarding shift symmetry and high-energy scattering amplitude constraints for determining Kerr black hole Wilson coefficients.

Conclusions:

• The scattering-amplitudes-based framework effectively determines two-body Hamiltonians for arbitrary spin systems, bypassing known theoretical difficulties.
• The inclusion of additional operators and higher-order spin contributions refines the description of binary dynamics.
• The proposed conjecture offers a pathway to all-orders spin-dependent calculations for Kerr black holes, consistent with existing results.