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Recent works have used a linear birth metallicity gradient to estimate theevolution of the [Fe/H] profile in the Galactic disk over time, and inferstellar birth radii (R$_\text{birth}$) from [Fe/H] and age measurements. Theseestimates rely on the evolution of [Fe/H] at the Galactic center ([Fe/H](0,$\tau$)) and the birth metallicity gradient ($\nabla$[Fe/H]($\tau)$) over time-- quantities that are unknown and inferred under key assumptions. In thiswork, we use the sample of Milky Way/Andromeda analogues from the TNG50simulation to investigate the ability to recover [Fe/H](R, $\tau$) andR$_\text{birth}$ in a variety of galaxies. Using stellar disk particles, wetest the assumptions required in estimating R$_\text{birth}$, [Fe/H](0,$\tau$), and $\nabla$[Fe/H]($\tau)$ using recently proposed methods tounderstand when they are valid. We show that $\nabla$[Fe/H]($\tau)$ can berecovered in most galaxies to within 22% from the range in [Fe/H] across age,with better accuracy for more massive and stronger barred galaxies. We alsofind that the true central metallicity is unrepresentative of the genuine disk[Fe/H] profile; thus we propose to use a projected central metallicity instead.About half of the galaxies in our sample do not have a continuously enrichingprojected central metallicity, with a dilution in [Fe/H] correlating withmergers. Most importantly, galaxy-specific [Fe/H](R, $\tau$) can be constrainedand confirmed by requiring the R$_\text{birth}$ distributions of mono-age,solar neighborhood populations to follow inside-out formation. We conclude thatexamining trends with R$_\text{birth}$ is valid for the Milky Way disk andsimilarly structured galaxies, where we expect R$_\text{birth}$ can berecovered to within 16% assuming today's measurement uncertainties in TNG50.

Empirical derivation of the metallicity evolution with time and radius using TNG50 Milky Way/Andromeda analogues