Properties of Wormhole Solutions of Einstein’s field equations for the Levi-Civita metric

Previous investigations of the Levi-Civita (LC) Effect [1] in the polarizable vacuum have shown that the spacetime geometry of the spatial part of the LC metric [2] describes a three-metric of a hypercylinder S² x Ɍ that can be interpreted as a special class of wormhole [3]. This hypercylinder metric has a position dependent gravitational potential possessing no asymptotically flat region, no flared-out wormhole mouth and no wormhole throat. From the Einstein field equations, we derive the non-trivial curvature invariants of a LC metric. We examine these curvature invariants to determine the similarities and differences of the LC metric to the better known metrics of Lorentzian Traversable Wormholes [4].

References:

[1] H.E. Puthoff, Claudio Maccone, E.W. Davis, “Levi-Civita Effect in the polarizable vacuum (PV) representation of general relativity,” arXiv:0403064 [physics.gen-ph].

[2] M. Morris and K. Thorn, Am. J. Phys. 56 (1988) 395.

[3] C. Maccone, “SETI Via Wormholes,” Proc. 47th Intern’l Astronautical Fed. (IAF) Congress, Beijing, 1996.

[4] B. Mattingly, A. Kar, M.D. Ali, A. Baas, C. Elmore, C. Watson, B. Shakerin, E. Davis, G. Cleaver, “Curvature Invariants for Lorentzian Traversable Wormholes,” arXiv:1806.10985[gr-gc].