Conservative Binary Dynamics at Order α^{5} in Electrodynamics.

We compute the potential-photon contributions to the classical relativistic scattering angle of two charged nonspinning bodies in electrodynamics through fifth order in the coupling. We use the scattering amplitudes framework, effective field theory, and multiloop integration techniques based on integration by parts and differential equations. At fifth order, the result is expressed in terms of cyclotomic polylogarithms.

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

We use a previously developed scattering-amplitudes-based framework for determining two-body Hamiltonians for generic binary systems with arbitrary spin S. By construction this formalism bypasses difficulties with unphysical singularities or higher-time derivatives. This framework has been previously used to obtain the exact velocity dependence of the O(G^{2}) quadratic-in-spin two-body Hamiltonian.

Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at O(G^{4}).

We complete the calculation of conservative two-body scattering dynamics at fourth post-Minkowskian order, i.e., O(G^{4}) and all orders in velocity, including radiative contributions corresponding to the tail effect in general relativity.

Scattering Amplitudes and Conservative Binary Dynamics at O(G^{4}).

Using scattering amplitudes, we obtain the potential contributions to conservative binary dynamics in general relativity at fourth post-Minkowskian order O(G^{4}). As in previous lower-order calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves polylogarithms with up to transcendental weight two and elliptic integrals.

Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order.

We present the amplitude for classical scattering of gravitationally interacting massive scalars at third post-Minkowskian order. Our approach harnesses powerful tools from the modern amplitudes program such as generalized unitarity and the double-copy construction, which relates gravity integrands to simpler gauge-theory expressions. Adapting methods for integration and matching from effective field theory, we extract the conservative Hamiltonian for compact spinless binaries at third post-Minkowskian order.