2020/10/31 by Brandon Mattingly, Abinash Kar, Matthew Gorban +11
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Computer science #Constant (computer programming) #Constant curvature #Cosmology and Gravitation Theories #Curvature #Field (mathematics) #Function (biology) #Geometry #Mathematics #Mean curvature #Mean curvature flow #Physics #Programming language #Pure mathematics #Radius of curvature #Relativity and Gravitational Theory #Theoretical physics #Warp drive #gr-qc
paper · pdf · doi:10.3390/universe7020021
published as Universe 2021, 7, 21 · 41 Pages, 15 figures
openalex publication_date 2021/01/20 · arxiv created 2021/04/14 · arxiv updated 2021/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A process for using curvature invariants is applied to evaluate the metrics for the Alcubierre 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 such spacetimes is unexplored. This paper uses the methods of computing and plotting the warp drive curvature invariants to reveal these spacetimes. The warp drive parameters of velocity, skin depth and radius are varied individually and then plotted to see each parameter’s unique effect on the surrounding curvature. For each warp drive, this research shows a safe harbor and how the shape function forms the warp bubble. The curvature plots for the constant velocity Natário warp drive do not contain a wake or a constant curvature, indicating that these are unique features of the accelerating Natário warp drive.