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

TL;DR

This paper critiques recent claims of testing extra dimensions using Sagittarius A*'s black hole shadow, emphasizing the limitations of current observational data and proposing future avenues for fundamental physics tests.

Contribution

It clarifies the invalidity of previous assumptions about shadow similarity and highlights the need for more comprehensive observables in future tests.

Findings

Current Sgr A* data do not support limits on shadow deviation from circularity.

Future observations of photon rings and azimuthal angle lapse will enable new tests.

Previous claims based on shadow similarity are invalid due to observational constraints.

Abstract

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. In the immediate future, the simplest tests of fundamental physics from Sgr A$^*$'s image will therefore mostly have to rely on $r_{\rm sh}$, whereas additional observables such as the photon ring and azimuthal angle lapse should soon be available and allow for novel tests.