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.

9 pages, 4 figures

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• Gravitational Lensing and Image Distortion by Buchdahl Inspired Metric in ${\mathcal{R}}^2$ Gravity
• Observational tests of asymptotically flat ${\mathcal{R}}^2$ spacetimes
• Observational test of ${\mathcal{R}}^2$ spacetimes with the S2 star in the Milky Way galactic center
• Epicyclic oscillations and accretion disk around a special Buchdahl-inspired spacetime
• Non-triviality of asymptotically flat Buchdahl-inspired metrics in pure $R^2$ gravity