Reducing the two-body problem in scalar-tensor theories to the motion of a test particle : a scalar-tensor effective-one-body approach

Abstract

Starting from the second post-Keplerian (2PK) Hamiltonian describing the conservative part of the two-body dynamics in massless scalar-tensor (ST) theories, we build an effective-one-body (EOB) Hamiltonian which is a $\nu$-deformation (where $\nu= 0$ is the test mass limit) of the analytically known ST Hamiltonian of a test particle. This ST-EOB Hamiltonian leads to a simple (yet canonically equivalent) formulation of the conservative 2PK two-body problem, but also defines a resummation of the dynamics which is well-suited to ST regimes that depart strongly from general relativity (GR) and which may provide information on the strong-field dynamics, in particular, the ST innermost stable circular orbit (ISCO) location and associated orbital frequency. Results will be compared and contrasted with those deduced from the ST-deformation of the (5PN) GR-EOB Hamiltonian previoulsy obtained in [Phys. Rev. D95, 124054 (2017)].