Calculation and Analysis of the Curvature Invariants for Traversable Lorentzian Wormholes and for Warp Metrics

Author: Gerald Cleaver, Ph.D. Early Universe Cosmology & String Theory, Professor and Graduate Program Director, Dept. of Physics & Center for Astrophysics, Baylor University

Abstract Background: In their classic papers, Morris and Thorne and Morris, Thorne, and Yurtsever were the first to analyze traversability of a classical wormhole. They studied the question of what the properties of a classical wormhole would have to be in order for the wormhole to be traversable by a human without fatal effects on the traveler.

Abstract Objectives: We present a process for applying the full set of spacetime curvature invariants as a new means to evaluate the traversability of Lorentzian wormholes and also of warped spacetime manifolds. This approach was formulated by Henry, Overduin, and Wilcomb for black holes.

Abstract Methods: Curvature invariants are independent of coordinate basis, so the process is free of coordinate mapping distortions and the same regardless of your chosen coordinates. The thirteen independent G’eh’eniau and Debever (GD) invariants are calculated for a given metric and the non-zero, independent curvature invariant functions are plotted and displayed. Four example traversable wormhole metrics are investigated: (i) thin shell at-face, (ii) spherically symmetric Morris and Thorne, (iii) thin-shell Schwarzschild, and (iv) Levi-Civita. We similarly calculate and display the curvature invariants for Alcubierre and Natario Warp Drive metrics. Both the constant velocity and accelerating Alcubierre and Natario metrics are presented.

Abstract Results: The wormholes are shown not to contain within physical bounds any internal divergences. The invariants plots demonstrate very non-trivial and non-intuitive time evolution dynamics of the warp bubbles.

Abstract Conclusions: The wormholes investigated are (at least theoretically) traversable.