We present a new approach to the conservative dynamics of binary systems, within the effective one-body (EOB) framework, based on the use of a Lagrange multiplier to impose the mass-shell constraint. When applied to the post-Minkowskian (PM) description of the two-body problem in Einsteinian gravity, this Lagrange-EOB (LEOB) approach allows for a new formulation of the conservative dynamics that avoids the drawbacks of the recursive definition of EOB-PM Hamiltonians. Using state-of-the-art values of the waveform and radiation reaction, based on factorized and resummed post-Newtonian (PN) expressions, we apply our new formalism to the construction of an aligned-spin, quasicircular, inspiralling EOB waveform model, called leob-pm, that incorporates analytical information up to the 4PM level, completed by 4PN contributions up to the sixth order in eccentricity, in the orbital sector, and by 4.5PN contributions, in the spin-orbit sector. In the nonspinning case, we find that an uncalibrated leob-pm model delivers maximum EOB/numerical relativity (NR) unfaithfulness ${\overline{\mathcal{F}}}_{\mathrm{EOBNR}}$ (with the Advanced LIGO noise in the total mass range $10-200M_{\odot }$) varying between 0.2% and 1% over all the nonspinning dataset of the Simulating Extreme Spacetime (SXS) Numerical Relativity catalog up to mass ratio $q=15$. It also delivers excellent phasing agreement with the $q=32$ configuration of the Rochester Institute of Technology catalog. We also found consistency between binding energies within a few percent at the NR merger location. Then, when NR informing the dynamics of the model (both orbital and spinning sectors) by using only 17 SXS dataset, we find that the EOB/NR unfaithfulness (compared to 530 spin-aligned SXS waveforms) has a median value of $5.39\times {10}^{-4}$, or $6.13\times {10}^{-4}$ (depending on the chosen description of spin-spin interactions), reaching at most $\sim 1\%$ in some of the high-spin corners. Although this global performance is less good (by a factor 3.67) than some of the state-of-the-art PN-Hamiltonian-based models, our finding shows that the LEOB approach is a promising route toward robustly incorporating both PM and PN information in the EOB description of the dynamics.

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• Gravitation
• Gravitational waves
• Classical black holes