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We determine the general local-in-time effective-one-body (EOB) Hamiltonian for massless Scalar-Tensor (ST) theories at third post-Newtonian (PN) order. For this, we first derive the order-reduced Lagrangian starting from the harmonic coordinate Lagrangian at the third post-Newtonian (PN) order and then obtain its corresponding centre of mass ordinary Hamiltonian. We then map the ordinary Hamiltonian to an effective-one-body (EOB) Hamiltonian at 3PN to derive the EOB metric potentials for the instantaneous part of the dynamics. We also explore the relevance of the 3PN scalar-tensor corrections by studying the innermost stable circular orbit (ISCO).

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Effective-One-Body Hamiltonian in Scalar-Tensor Gravity at the Third Post-Newtonian Order

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  • 发表日期：

    2025年

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  • Tamanna Jain

摘要

We determine the general local-in-time effective-one-body (EOB) Hamiltonian for massless Scalar-Tensor (ST) theories at third post-Newtonian (PN) order. For this, we first derive the order-reduced Lagrangian starting from the harmonic coordinate Lagrangian at the third post-Newtonian (PN) order and then obtain its corresponding centre of mass ordinary Hamiltonian. We then map the ordinary Hamiltonian to an effective-one-body (EOB) Hamiltonian at 3PN to derive the EOB metric potentials for the instantaneous part of the dynamics. We also explore the relevance of the 3PN scalar-tensor corrections by studying the innermost stable circular orbit (ISCO).