universe Article Curvature Invariants for the Alcubierre and Natário Warp Drives Brandon Mattingly 1,2 , Abinash Kar 1,2 , Matthew Gorban 1,2, William Julius 1,2, Cooper K. Watson 1,2, MD Ali 1,2, Andrew Baas 1,2, Caleb Elmore 1,2 , Jeffrey S. Lee 1,2 , Bahram Shakerin 1,2, Eric W. Davis 1,3 and Gerald B. Cleaver 1,2,* 1 Early Universe Cosmology and Strings (EUCOS) Group, Center for Astrophysics, Space Physics and Engineering Research (CASPER), Baylor University, Waco, TX 76798, USA;
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[email protected] (E.W.D.) 2 Department of Physics, Baylor University, Waco, TX 76798, USA 3 Institute for Advanced Studies at Austin, 11855 Research Blvd., Austin, TX 78759, USA * Correspondence:
[email protected] Abstract: A process for using curvature invariants is applied to evaluate the metrics for the Alcu- bierre and the Natário warp drives at a constant velocity. Curvature invariants are independent of coordinate bases, so plotting these invariants will be free of coordinate mapping distortions. As a consequence, they provide a novel perspective into complex spacetimes, such as warp drives. Warp drives are the theoretical solutions to Einstein’s field equations that allow for the possibility for faster-than-light (FTL) travel. While their mathematics is well established, the visualisation of Citation: Mattingly, B.; Kar, A.; such spacetimes is unexplored.