Note on Fundamental Physics Tests from Black Hole Imaging: Comment on "Hunting for Extra Dimensions in the Shadow of Sagittarius A*"

Several recent works have tested fundamental physics with horizon-scale black hole (BH) images, using the size rsh and deviation from circularity ΔC of the BH shadow. For the Event Horizon Telescope image of Sgr A*, limits on ΔC are not available due to the sparse interferometric coverage of the 2017 observations, alongside the short variability timescale of Sgr A* compared to M87*. We comment on the results of a recent preprint which purports to have derived new limits on extra dimensions using the deviation from circularity of Sgr A*'s shadow. The latter is quoted to be ≲10% as with M87*, based on the "similarity" of the two shadows, which however is an incorrect assumption. In the immediate future, the simplest tests of fundamental physics from Sgr A*'s image will mostly have to rely on rsh.