A stationary axisymmetric vacuum solution for pure $R^2$ gravity

Abstract: The closed-form expression for pure $\mathcal{R}^{2}$ vacuum solution obtained in Phys. Rev. D \textbf{107}, 104008 (2023) lends itself to a generalization to axisymmetric setup via the modified Newman--Janis algorithm. We adopt the procedure put forth in Phys. Rev. D \textbf{90}, 064041 (2014) bypassing the complexification of the radial coordinate. The procedure presumes the existence of Boyer-Lindquist coordinates. Using the Event Horizon Telescope Collaboration results, we model the central black hole M87{} by the thus obtained exact rotating metric, depending on the mass, rotation parameter and a third dimensionless parameter. The latter is constrained upon investigating the shadow angular size assuming mass and rotation parameters are those of M87{}. Stability is investigated.