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Conservative dynamics of relativistic binaries beyond Einstein gravity

Jordan Wilson-Gerow

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Phys. Rev. D 112, 044004 – Published 4 August, 2025

DOI: https://doi.org/10.1103/99k7-whlt

Abstract

We study the conservative dynamics of spinless compact objects in a general effective theory of gravity, which includes a metric and an arbitrary number of scalar fields, through O(G3). Departures from Einstein gravity, which preserve general coordinate and local Lorentz invariance, are characterized by higher-derivative terms in a Lagrangian whose coupling constants scale as powers of a “new-physics” length scale, ℓ. For a purely metric theory we compute the contributions from the leading and subleading higher-curvature curvature corrections. In four dimensions these are cubic and quartic curvature terms, i.e. orders ℓ4 and ℓ6. We also study a general multi-scalar-tensor theory of gravity to order ℓ4, which includes both Einstein-dilaton-Gauss-Bonnet and dynamical Chern-Simons higher-order couplings. Specifically, we compute the radial action in a post-Minkowskian approximation for scattering orbits to the two-loop order. The result encodes the fully relativistic dynamics of the compact objects and serves as a generating function for gauge-invariant orbital observables for both bound and unbound binary systems. Where overlapping post-Newtonian results are available, we have verified agreement.

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Phys. Rev. D 112, 044004– Published 4 August, 2025
  • Received 7 March 2025
  • Accepted 15 July 2025
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