Higher-order Buchdahl-inspired corrections to the timing model

Derive the coefficients and time dependence of the higher-order Buchdahl-inspired terms beyond the first post-Newtonian expansion in order to establish a rigorous theoretical-error estimate for pulsar-timing constraints on the deviation parameter ε.

Background

The pulsar-timing forecast is constructed using a weak-field Buchdahl-inspired metric and orbital dynamics truncated at first post-Newtonian order. For an S2-like orbit, the forecasted sensitivity to the deviation parameter ε is of order 10⁻⁴, comparable to the estimated scale of generic omitted higher-order post-Newtonian terms.

Because the coefficients and time dependence of the higher-order Buchdahl-inspired contributions are not known, the estimated truncation scale cannot presently be interpreted as a rigorous theoretical-error bound. Applying the forecast to real observations would therefore require a higher-order extension of the timing model or an explicit treatment of theoretical uncertainty.