Curvature Invariants for Lorentzian Traversable Wormholes

A process for using curvature invariants is applied as a new means to evaluate the traversability of Lorentzian wormholes. This approach was formulated by Henry, Overduin and Wilcomb for Black Holes in Reference [1]. Curvature invariants are independent of coordinate basis, so the process is free of coordinate mapping distortions. The fourteen G'eh'eniau and Debever (GD) invariants are calculated and the non-zero, independent curvature invariant functions are plotted. Three example traversable wormhole metrics (i) thin-shell flat-face, (ii) spherically symmetric Morris and Thorne, and (iii) thin-shell Schwarzschild wormholes are investigated and are demonstrated to be traversable.

[1] Henry, R. C., Overduin, J. and Wilcomb K. (2016), "A New Way to See Inside Black Holes," arXiv:1512.02762v2 [gr-qc].