Closed Timelike Curves Induced by a Buchdahl-Inspired Vacuum Spacetime in R2 Gravity

Abstract

The recently obtained special Buchdahl-inspired metric Phys. Rev. D 107, 104008 (2023) describes asymptotically flat spacetimes in pure Ricci-squared gravity. The metric depends on a new (Buchdahl) parameter k˜ of higher-derivative characteristic, and reduces to the Schwarzschild metric, for k˜=0. For the case k˜∈(−1,0), it was shown that it describes a traversable Morris–Thorne–Buchdahl (MTB) wormhole Eur. Phys. J. C 83, 626 (2023), where the weak energy condition is formally violated. In this paper, we briefly review the special Buchdahl-inspired metric, with focuses on the construction of the Kruskal–Szekeres (KS) diagram and the situation for a wormhole to emerge. Interestingly, the MTB wormhole structure appears to permit the formation of closed timelike curves (CTCs). More specifically, a CTC straddles the throat, comprising of two segments positioned in opposite quadrants of the KS diagram. The closed timelike loop thus passes through the wormhole throat twice, causing two reversals in the time direction experienced by the (timelike) traveller on the CTC. The key to constructing a CTC lies in identifying any given pair of antipodal points (T,X) and (−T,−X) on the wormhole throat in the KS diagram as corresponding to the same spacetime event. It is interesting to note that the Campanelli–Lousto metric in Brans–Dicke gravity is known to support two-way traversable wormholes, and the formation of the CTCs presented herein is equally applicable to the Campanelli–Lousto solution.

End of Time Travel

“…The idea that CTC has physical existence is still actual. In a recent article, physicists are discussing that time travel is possible through wormholes [5]. The idea that time travel will be possible once in the future was also published in 1988: "It is argued that, if the laws of physics permit an advanced civilization to create and maintain a wormhole in space for interstellar travel, then that wormhole can be converted into a time machine with which causality might be violated.…”

Extension of Buchdahl’s Theorem on Reciprocal Solutions

“…Buchdahl's work has inspired much research over the years [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] (we refer the reader to [32] for a recent review). Here, we extend Buchdahl's method to incorporate the cosmological constant, thereby, with a conformal transformation of the metric, obtaining solutions for a version of Brans-Dicke theory that includes a quadratic potential.…”