Note on fundamental physics tests from black hole imaging: Comment on "Hunting for extra dimensions in the shadow of Sagittarius A$^*$"

Understand

Several works over the past years have discussed the possibility of testing fundamental physics using Very Long Baseline Interferometry horizon-scale black hole (BH) images, such as the Event Horizon Telescope (EHT) images of M87$^*$ and Sagittarius A$^*$ (Sgr A$^*$), using the size $r_{\rm sh}$ and deviation from circularity $\Delta \mathcal{C}$ of the BH shadow.

• For the case of the EHT image of Sgr A$^*$, limits on $\Delta \mathcal{C}$ are not available due to the sparse interferometric coverage of the 2017 observations, alongside the short variability timescale of Sgr A$^*$ compared to M87$^*$.
• Concerning this point, 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 $\lesssim 10\%$ as with M87$^*$, based on the "similarity" of the two shadows: however, this is an incorrect assumption, invalidating the subsequent results.