No-Hair Theorem in the Wake of Event Horizon Telescope

Thanks to the release of the extraordinary EHT image of shadow attributed to the M87* supermassive black hole (SMBH), we have a novel window to assess the validity of fundamental physics in the strong-field regime. Motivated by this, we consider Johannsen \& Psaltis metric parameterized by mass, spin, and an additional dimensionless hair parameter $\epsilon$ which in the high rotation regimes is able to provide a suitable framework for the test of the no-hair theorem (NHT) using the EHT data. Incorporating the $\epsilon$ into the standard Kerr spacetime enrich it in the sense that, depending on setting the positive and negative values for that, we deal with alternative compact objects: deformed Kerr naked singularity and Kerr BH solutions, respectively. Shadows associated with these two possible solutions indicate that the deformation parameter $\epsilon$ affects the geometry shape of standard shadow such that it become more oblate and prolate with $\epsilon 0$, respectively. By scanning the window associated with three shadow observables: oblateness, deviation from circularity, and shadow diameter, we perform a numerical analysis within the range $a_*=0.9\mp0.1$ of the dimensionless rotation parameter, to find the constraints on the hair parameter $\epsilon$ in both possible solutions. For both possible signs of $\epsilon$, we extract a variety of upper bounds that are in interplay with $a_*$. Our analysis suggests that as the rotation parameter approaches the extreme limit, although the allowable range of both hair parameters becomes narrower, the hairy Kerr BH solution is a more promising candidate to play a role of the alternative compact object instead of standard Kerr BH. The lack of tension between hairy Kerr BH with the current observation of the EHT shadow of the M87* SMBH carries this message that the possibility of NHT violation is not excluded.