Testing black hole mimickers with the Event Horizon Telescope image of Sagittarius A$^*$

The Event Horizon Telescope (EHT) has recently observed the image and shadow of the supermassive compact object Sagittarius A$^*$ (Sgr A$^*$). According to the EHT collaboration, the observed image is consistent with the expected appearance of a Kerr black hole. However, it is well-known that some non-Kerr objects may mimic many of the properties of the Kerr black hole, and hence, their shadows might be consistent with the observed shadow of Sgr A$^*$. In this work, we consider two black hole mimickers and study their shadows. The first mimicker is a rotating generalisation of the recently proposed static, spherically symmetric black-bounce spacetime by Simpson and Visser where the central Schwarzschild singularity is replaced by a minimal surface. The second one is the $\gamma$-metric which is a static, axially symmetric singular solution of the vacuum Einstein's equations without an event horizon. We put constraint on the parameters of these black hole mimickers by comparing their shadows with the one observed for Sgr A$^*$.