No-hair theorem in the wake of Event Horizon Telescope
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Abstract
Thanks to the release of the extraordinary EHT image of shadow attributed to\nthe M87* supermassive black hole (SMBH), we have a novel window to assess the\nvalidity of fundamental physics in the strong-field regime. Motivated by this,\nwe consider Johannsen \\& Psaltis metric parameterized by mass, spin, and an\nadditional dimensionless hair parameter $\\epsilon$. This parametric framework\nin the high rotation regimes provides a well-behaved bed to the strong-gravity\ntest of the no-hair theorem (NHT) using the EHT data. Incorporating the\n$\\epsilon$ into the standard Kerr spacetime enrich it in the sense that,\ndepending on setting the positive and negative values for that, we deal with\nalternative compact objects: deformed Kerr naked singularity and Kerr BH\nsolutions, respectively. Shadows associated with these two possible solutions\nindicate that the deformation parameter $\\epsilon$ affects the geometry shape\nof standard shadow such that it becomes more oblate and prolate with\n$\\epsilon<0$ and $\\epsilon>0$, respectively. By scanning the window associated\nwith three shadow observables oblateness, deviation from circularity, and\nshadow diameter, we perform a numerical analysis within the range\n$a_*=0.9\\mp0.1$ of the dimensionless rotation parameter, to find the\nconstraints on the hair parameter $\\epsilon$ in both possible solutions. For\nboth possible signs of $\\epsilon$, we extract a variety of upper bounds that\nare in interplay with $a_*$. Although by approaching the rotation parameters to\nthe extreme limit, the allowable range of both hair parameters becomes\nnarrower, the hairy Kerr BH solution is a more promising candidate to play the\nrole of the alternative compact object instead of the standard Kerr BH. The\nlack of tension between hairy Kerr BH with the current observation of the EHT\nshadow of the M87* SMBH carries this message that there is the possibility of\nNHT violation.\n