Buchdahl-inspired spacetimes and wormholes: Unearthing Hans Buchdahl’s other “hidden” treasure trove

Abstract

Circa 1962 Hans A. Buchdahl pioneered a program — and made significant progress — seeking vacuo configurations in pure [Formula: see text] gravity (H. A. Buchdahl, Nuovo Cimento 23 (1962) 141). 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 [Formula: see text] vacua that he sought were within his striking distance. In our recent three-paper body of work published in Nguyen (Phys. Rev. D 106 (2022) 104004; Phys. Rev. D 107 (2023) 104008; Phys. Rev. D 107 (2023) 104009), 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. May this unsung legacy of Hans A. Buchdahl long “forsaken” and “forgotten” finally live on Our essay is a passageway bridging the past and the future. The past is rooted in a research program originated but left unfinished by Buchdahl going back threescore years ago. The future is the new horizons his program brings forth. In between is our labor — summarized in a three-installment “Beyond Schwarzschild–de Sitter spacetimes” series[1–3] — to advance the Buchdahl program and achieve his ultimate goal.