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B[e] supergiants have unusual circumstellar environments which may includethin, concentric rings displaying atomic line emission. GG Carinae is a B[e]supergiant binary which exhibits such a geometry in its circumbinaryenvironment. We study atomic emission lines arising from GG Carinae'scircumbinary disc in FEROS spectra collected between 1998 and 2015. We findthat semi-forbidden Fe\,II] and permitted Ca\,II emission are formed in thesame thin circumbinary ring previously reported to have forbidden [O\,I] and[Ca\,II] emission. We find that there are two circumbinary rings orbiting withprojected velocities of $84.6\pm1.0$\,km\,s$^{-1}$ and$27.3\pm0.6$\,km\,s$^{-1}$. Deprojecting these velocities from theline-of-sight, and using updated binary masses presented by\cite{Porter2021GGPhotometry}, we find that the radii of the circumbinary ringsare $2.8^{+0.9}_{-1.1}$\,AU and $27^{+9}_{-10}$\,AU for the inner ring andouter ring respectively. We find evidence of subtle dynamical change in theinner circumbinary ring over the 17 years spanned by the data, manifesting invariability in the ratio of the intensity of the blueshifted peak to theredshifted peak of its emission lines and the central velocity becoming moreblueshifted. We perform smoothed-particle hydrodynamic simulations of thesystem which suggest that these observed changes are consistent with pumping ofthe eccentricity of a radially thin circumbinary ring by the inner binary. Wefind a systemic velocity of the GG Carinae system of $-23.2 \pm0.4$\,km\,s$^{-1}$.

The circumbinary rings of GG Carinae: indications of disc eccentricity growth in the B[e] supergiant's atomic emission lines