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arXiv · 2510.11836

Shift vector sign reversal in the Alcubierre warp drive spacetime geometry and nonlinear Burgers-type dynamics

Osvaldo L. Santos-Pereira·Everton M. C. Abreu·Marcelo B. Ribeiro
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Abstract

This work investigates a sign reversal of the shift vector in the Alcubierre Warp Drive geometry and its effect on the nonlinear reduced structure of the Einstein equations. Previous analyses showed that Burgers-type equations can arise in warp drive spacetimes, leading to vacuum solutions under suitable assumptions on the sign of the shift vector and on matter-source reductions. Here, we analyze the original Alcubierre shift-vector sector and show that, under an appropriate mathematical ansatz, the $\{22\}$ and $\{33\}$ components of the Einstein equations can be formally decomposed into viscous Burgers-type and heat-type equations. The resulting heat-type structure and the constant analogous to a diffusivity coefficient constitute new formal features of the reduced shift-vector dynamics. Since these terms are introduced through an ansatz and are not generated by a specific energy-momentum tensor source, they should not be interpreted as physical diffusivity without an additional matter model. The vacuum reductions of the Einstein equations for the warp-drive geometry come with an important caveat: the shift vector must depend only on time and on one spatial coordinate, namely $\beta(t,x)$. Consequently, the Alcubierre regulating function no longer retains its original spherical dependence on $r_s(t)$, and the resulting solutions should be interpreted as lower-dimensional shift-sector reductions rather than complete spherically symmetric warp bubble configurations.

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Osvaldo L. Santos-Pereira, Everton M. C. Abreu, Marcelo B. Ribeiro. 2025-10-13. Shift vector sign reversal in the Alcubierre warp drive spacetime geometry and nonlinear Burgers-type dynamics. https://doi.org/10.1140/epjp%2Fs13360-026-08079-5

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