A stationary axisymmetric vacuum solution for pure ² gravity

Abstract

The closed-form expression for pure  2 vacuum solution obtained in Phys. Rev. D 107, 104 008 (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 90, 064 041 (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.