Physical explanation of inertial-like dynamical friction

Investigate the physical origin of the proportionality between the maximum dynamical-friction force and the product of scalar-field mass and black-hole acceleration, namely $F_\star \propto m a$, and determine why the force exhibits this inertial-like behavior.

Background

For accelerating black holes modeled by the C-metric, the simulations report that the force initially grows, reaches a maximum value $F_\star$, and then decreases sharply. The maximum force is fitted as proportional to the acceleration, while the slope of this relationship is itself proportional to the mass $m$ of the scalar field, suggesting $F_\star \propto m a$.

The paper identifies this proportionality as a nontrivial result but does not provide a physical explanation for it. The unresolved problem is therefore to develop an analytical or otherwise physically grounded account of how scalar-field mass and black-hole acceleration combine to produce the observed maximum force.