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arXiv · 2211.15580

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

Tamanna Jain·Piero Rettegno·Michalis Agathos·Alessandro Nagar·Lorenzo Turco
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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.

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Tamanna Jain, Piero Rettegno, Michalis Agathos, Alessandro Nagar, Lorenzo Turco. 2022-11-28. Effective one body Hamiltonian in scalar-tensor gravity at third post-Newtonian order. https://doi.org/10.1103/physrevd.107.084017

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