Authors: Fernando Loup
Warp Drives are solutions of the Einstein Field Equations that allows superluminal travel within the framework of General Relativity. There are at the present moment two known solutions: The Alcubierre warp drive discovered in $1994$ and the Natario warp drive discovered in $2001$.Alcubierre used the so-called $3+1$ original Arnowitt-Dresner-Misner($ADM$) formalism using the approach of Misner-Thorne-Wheeler to develop his warp drive theory.As a matter of fact the first equation in his warp drive paper is derived precisely from the original $3+1$ $ADM$ formalism and we have strong reasons to believe that Natario which followed the Alcubierre steps also used the original $3+1$ $ADM$ formalism to develop the Natario warp drive spacetime.Several years ago some works appeared in the scientific literature advocating two new parallel $3+1$ $ADM$ formalisms.While the original $ADM$ formalism uses mixed contravariant and covariant scripts one of the new parallel formalisms uses only contravariant scripts while the other uses only covariant scripts.Since the Natario vector is the generator of the Natario warp drive spacetime metric in this work we expand the original Natario vector including the coordinate time as a new Canonical Basis for the Hodge star generating an expanded Natario vector and we present $6$ equations for the Natario warp drive spacetime $3$ of them with constant velocities one for the original $ADM$ formalism and $2$ other for the parallel formalisms. We also present the corresponding $3$ extended versions of the Natario warp drive spacetime metric which encompasses accelerations and variable velocities both in the original and parallel $ADM$ formalisms.
Comments: 79 Pages.
[v1] 2018-08-27 23:38:11
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