Non-triviality of an asymptotically flat vacuum spacetime in pure R2 gravity

In Phys. Rev. D 107, 104008 (2023), we reported a novel exact closed-form solution which describes asymptotically flat spacetimes in pure Formula: see text gravity. The solution is Ricci scalar flat, viz. Formula: see text everywhere. Whereas any metric with a null Ricci scalar would trivially satisfy the Formula: see text vacuo field equation, Formula: see text, in this paper, we shall show that our solution satisfies a “stronger” version of the Formula: see text vacuo field equation, viz. Formula: see text, despite the term Formula: see text being singular. Even though Formula: see text identically vanishes, for our solution, the combinations Formula: see text and Formula: see text are free of singularity. This exceptional property sets our solution apart from the set of null-Ricci-scalar metrics and makes it a genuinely nontrivial solution. We further demonstrate that, as a member of a larger class of asymptotically de Sitter metrics, our solution is resilient against perturbations in the scalar curvature at largest distances, making it relevant for physical situations where the background deviates from asymptotic flatness.