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

Abstract

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.