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We present a 2-dimensional chemical evolution code applied to a Milky Way type galaxy, incorporating the role of spiral arms in shaping azimuthal abundance variations, and confront the predicted behaviour with recent observations taken with integral field units. To the usual radial distribution of mass, we add the surface density of the spiral wave and study its effect on star formation and elemental abundances. We compute five different models: one with azimuthal symmetry which depends only on radius, while the other four are subjected to the effect of a spiral density wave. At early times, the imprint of the spiral density wave is carried by both the stellar and star formation surface densities; conversely, the elemental abundance pattern is less affected. At later epochs, however, differences among the models are diluted, becoming almost indistinguishable given current observational uncertainties. At the present time, the largest differences appear in the star formation rate and/or in the outer disc (R$\ge$ 18\,kpc). The predicted azimuthal oxygen abundance patterns for $t \le 2$\,Gyr are in reasonable agreement with recent observations obtained with VLT/MUSE for NGC 6754, Comment: 19 pages, 12 figures, MNRAS to be published

A reformulation of the Schwarzschild solution of the linearised Einstein field equations in post-Riemannian Finsler spacetime is derived. The solution is constructed in three stages: the exterior solution, the event-horizon solution and the interior solution. It is shown that the exterior solution is asymptotically similar to Newtonian gravity at large distances implying that Newtonian gravity is a low energy approximation of the solution. Application of Eddington-Finklestein coordinates is shown to reproduce the results obtained from standard general relativity at the event horizon. Further application of Kruskal-Szekeres coordinates reveals that the interior solution contains maximally extensible geodesics., Comment: 9 pages