Comment on "Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A*"

Abstract

Vagnozzi et al. constrained the additional parameter of spacetimes with a photon sphere from the observation of the shadow of Sagittarius A* under the assumption that a distance to the Sagittarius A* and its mass parameter was estimated from other observations. They claimed that a Damour-Solodukhin wormhole with an additional parameter $\lambda$ is not an asymptotically-flat spacetime and that they gave the first robust observational constraint on the parameter $\lambda$ of the Damour-Solodukhin wormhole. However, they overlooked the fact that: (A) the Damour-Solodukhin wormhole spacetime is asymptotically flat, (B) the throat of the Damour-Solodukhin wormhole works as an effective photon sphere for $\lambda>\sqrt{2}/2$, and (C) not only a usual mass parameter but also the parameter $\lambda$ contributes the mass of the Damour-Solodukhin wormhole. Because of the overlook (C), we realize that their constraint on the parameter $\lambda$ is invalid. This is because their method corresponds to the following way: They estimated the mass parameter from the other observations under the assumption $\lambda=0$ even though the value of the parameter $\lambda$ strongly affects the determination of the mass parameter, and then, they used the value of the mass parameter to constrain $\lambda$ from the observation of the shadow. We conclude that we should constrain the mass parameter and $\lambda$ from the shadow observation and other observations without the assumption $\lambda=0$.