Binary systems of compact objects, such as black holes, serve as natural laboratories for testing General Relativity in strong-field regimes. Higher curvature corrections to General Relativity, like those described by scalar-Gauss-Bonnet (sGB) theory, are of particular interest. This theory introduces a scalar field dynamically coupled to curvature scalars, which can give rise to scalar condensates around black holes. Considering a mass for this scalar field is a natural extension that introduces new phenomenology and additional scales into the system.

Researchers have computed the dynamics of a binary system of nonspinning black holes in massive sGB theory using the post-Newtonian (PN) approximation. They obtained solutions for the equations of motion, center-of-mass transformation, and binding energy for circular and eccentric orbits up to 1PN order. For the first time, these calculations include higher curvature corrections coupled to scalar mass. While most calculations are valid for generic scalar masses, the final explicit expressions assume the scalar mass is small compared to the total mass of the binary, expanding to quadratic order in this ratio.

The results indicate that scalar mass corrections to the gauge-invariant binding energy feature terms of both same and opposite signs. In the perturbative limit, this leads to an overall decrease in the binding energy. The effects are most pronounced for binary systems with a high mass ratio and large eccentricity. These methods and results will be crucial for future computations of gravitational waves sourced by such systems, enabling more precise comparisons with observations from detectors like LIGO and Virgo, and helping to refine our understanding of gravity under extreme conditions.