Nonlocal-in-time effective one body Hamiltonian in scalar-tensor gravity at third post-Newtonian order

TL;DR

This paper extends the effective-one-body formalism for scalar-tensor gravity to third post-Newtonian order, incorporating nonlocal-in-time effects into the Hamiltonian to improve modeling of conservative dynamics.

Contribution

It derives the nonlocal-in-time EOB Hamiltonian for scalar-tensor theories at 3PN order by mapping from the nonlocal Lagrangian and reducing it to a local Hamiltonian form.

Findings

Derived the nonlocal-in-time EOB Hamiltonian at 3PN order.

Mapped nonlocal dynamics onto local Hamiltonian using order-reduction.

Determined corrections to EOB potentials $(A,B,Q_e)$ at 3PN.

Abstract

We complete the nonlocal-in-time effective-one-body (EOB) formalism of conservative dynamics for massless Scalar-Tensor (ST) theories at third post-Newtonian (PN) order. The nonlocal-in-time EOB Hamiltonian is obtained by mapping the order-reduced Hamiltonian corresponding to the nonlocal-in-time Lagrangian derived in [Phys. Rev. D 99, 044047 (2019)]. To transcribe the dynamics within EOB formalism, we use a strategy of order-reduction of nonlocal dynamics to local ordinary action-angle Hamiltonian. We then map this onto the EOB Hamiltonian to determine the nonlocal-in-time ST corrections to the EOB potentials $(A,B,Q_e)$ at 3PN order.