Absolute force normalization across separations

Determine the absolute strength of the gravitational force between the positive- and negative-active-mass soliton stars at separations other than d = 10 by performing a converged separation scan, thereby establishing whether the normalization a = M̄/d² holds across the full separation range.

Background

The paper measures the acceleration–separation exponent using a scan over d = 8–20, obtaining a result consistent with d⁻². However, all points in that scan use the base grid, which underestimates the absolute acceleration by approximately 7% at d = 10. Consequently, the exponent and relative trends are considered reliable, while the absolute force normalization away from the reference separation remains unresolved. A converged separation scan is identified as the natural next step.

References

What is not established. Four things remain open.

The Bondi Dipole in Full Numerical Relativity: a Self-Accelerating Positive-Negative Mass Binary  (2608.24577 - Shirokov, 25 Aug 2026) in Section VIII, paragraph beginning “What is not established”