  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.
