Analysis of the Curvature Invariants for the Natario Warp Metric

A process for using curvature invariants is applied as a new means to evaluate the Natario Warp Drive Metric [1]. This approach was formulated by Henry et al. for Black Holes [2] and was further generalized to accommodate the case of Lorentzian Traversable Wormholes by Mattingly et al. [3]. Curvature invariants are independent of coordinate basis, so the process is free of coordinate mapping distortions. Thirteen curvature invariants are calculated and the non-trivial ones are plotted. The constant velocity and accelerating Natario metrics [4] are examined. The dynamics of the warp bubble as it evolves in time is analyzed by plotting the invariants. A spaceship may harbour in the interior of the warp bubble, which the invariant plots show to be flat and free of any fluctuations.

[1] Natario, J. "Warp Drive with Zero Expansion", Classical and Quantum Gravity 19 (2002) 1157-1166

[2] Henry, R. et al. (2016), "A New Way to See Inside Black Holes", arXiv:1512.02762v2 [gr-qc]

[3] Mattingly, B. et al. (2018), "Curvature Invariants for Lorentzian Traversable Wormholes", arXiv:1806.10985v1 [gr-qc]

[4] Loup, F. [Research Report hal-01655423] Residencia de Estudantes Universitas (2017)