Effective one body Hamiltonian in scalar-tensor gravity at third post-Newtonian order

TL;DR

This paper derives a third post-Newtonian order effective-one-body Hamiltonian for scalar-tensor theories, enabling more precise gravitational wave modeling and tests of gravity beyond General Relativity.

Contribution

It provides the first comprehensive 3PN EOB Hamiltonian for scalar-tensor theories, including corrections for finite-size and nonlocal effects, enhancing waveform accuracy.

Findings

Derived the 3PN scalar-tensor EOB potentials (A, B, Q_e).

Analyzed the impact of 3PN corrections on the innermost stable circular orbit frequency.

Facilitated high-precision gravitational waveform modeling in scalar-tensor theories.

Abstract

We determine the general local-in-time effective-one-body (EOB) Hamiltonian for massless Scalar-Tensor (ST) theories at third post-Newtonian (PN) order. Starting from the Lagrangian derived in [Phys. Rev. D 99, 044047 (2019)], we map it to the corresponding ordinary Hamiltonian describing the two-body interaction in ST theories at 3PN level. Using a canonical transformation, we then map this onto an EOB Hamiltonian so as to determine the ST corrections to the 3PN-accurate EOB potentials $(A,B,Q_e)$ at 3PN. We then focus on circular orbits and compare the effect of the newly computed 3PN terms, also completed with finite-size and nonlocal-in-time contributions, on predictions for the frequency at the innermost stable circular orbit. Our results will be useful to build high-accuracy waveform models in ST theory, which could be used to perform precise tests against General Relativity using gravitational wave data from coalescing compact binaries.