Constraints on Buchdahl-Inspired Gravity from Future Pulsar Timing near Sgr A*

Future pulsar timing observations near Sgr A* offer a unique probe of gravitational physics in the vicinity of a supermassive black hole. We forecast the ability of such measurements to constrain a Buchdahl-inspired R squared gravity, parameterized by a single deviation parameter ε, using a timing framework that self-consistently integrates orbital dynamics with light-propagation delays and preserves the full timing solution across the observing span. Through Fisher-matrix forecasts for a representative pulsar, we systematically isolate how the precision on ε depends on orbital geometry. We find that shorter orbital periods and higher eccentricities significantly enhance sensitivity, consistent with a substantial contribution from observations near periastron. As a benchmark comparison, we further consider a hypothetical pulsar on an S2-like orbit (P b=16 yr, e=0.88) and obtain a statistical sensitivity of σ ε about 10-4 within the adopted weak-field, static, and spherically symmetric timing model. This sensitivity is comparable to the natural order-of-magnitude truncation scale of the 1PN expansion and should not be interpreted as a complete forecast for the real Sgr A* system. Under the adopted idealized assumptions, the characteristic statistical scale is several orders of magnitude below the current S2 95% confidence interval half-width (ε S2 95% about 0.56), though this comparison is heuristic given the differing confidence levels. These trends provide quantitative guidance for target selection and campaign design in future Galactic-center pulsar searches.