Buchdahl-inspired spacetimes and wormholes: Unearthing Hans Buchdahl's other 'hidden' treasure trove

TL;DR

This paper uncovers a new class of non-Schwarzschild spacetimes and wormholes in quadratic gravity, completing Buchdahl's 1962 program and revealing novel phenomenology beyond Einstein's theory.

Contribution

It finalizes Buchdahl's 1962 quest by deriving vacua in pure R² gravity, introducing higher-derivative spacetimes and wormholes that extend beyond Einstein-Hilbert solutions.

Findings

Discovered non-Schwarzschild vacuum solutions in R² gravity.

Constructed Buchdahl-inspired wormholes with unique properties.

Revealed phenomenology surpassing traditional Einstein gravity.

Abstract

Circa 1962 Hans A. Buchdahl pioneered a program -- and made significant progress -- seeking vacuo configurations in pure $\mathcal{R}^{2}$ gravity [H. A. Buchdahl, Nuovo Cimento 23, 141 (1962)]. Unfortunately, he deemed the final step in his calculations impassable and prematurely suspended his pursuit. Since then, his achievements on this front have faded into dormancy. Unbeknownst to Buchdahl himself, the $\mathcal{R}^{2}$ vacua that he sought were within $\textit{his}$ striking distance. In our recent three-paper body of work published in Phys. Rev. D, we broke this six-decades-old impasse and accomplished his goal: A novel class of metrics, describing non-Schwarzschild spacetimes in quadratic gravity and carrying a hallmark of higher-derivative characteristic. Intriguing properties of Buchdahl-inspired spacetimes and their associated Morris-Thorne-Buchdahl wormholes -- summarized herein -- embody a new branch of phenomenology that transcends the Einstein-Hilbert paradigm.