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. This parametric framework in the high rotation regimes provides a well-behaved bed to the strong-gravity 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 becomes more oblate and prolate with epsilon < 0 and 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 -/+ 0.1 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(*). Although by approaching the rotation parameters to the extreme limit, the allowable range of both hair parameters becomes narrower, the hairy Kerr BH solution is a more promising candidate to play the role of the alternative compact object instead of the 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 there is the possibility of NHT violation.

Automated summary

The EHT image of the M87* supermassive black hole allows for a test of the no-hair theorem by introducing a hair parameter ε into the Kerr spacetime metric. The analysis shows that the ε parameter affects the geometry of the standard shadow, leading to different shapes depending on its positive or negative value. Numerical analysis within a specific range of rotation parameter provides constraints on the hair parameter in both possible solutions.