阿库别瑞引擎

数学形式

${\displaystyle ds^{2}=g_{ij}dx^{i}dx^{j}=-\left(\alpha ^{2}-\beta _{i}\beta ^{i}\right)\,dt^{2}+2\beta _{i}\,dx^{i}\,dt+\gamma _{ij}\,dx^{i}\,dx^{j}}$

${\displaystyle \alpha =1;\,}$
${\displaystyle \beta ^{1}=\beta ^{x}=-v_{s}(t)f\left(r_{s}(t)\right),\beta ^{2}=\beta ^{y}=0,\beta ^{3}=\beta ^{z}=0;\,}$
${\displaystyle \gamma _{ij}=\delta _{ij}={\begin{pmatrix}1&0&0\\0&1&0\\0&0&1\end{pmatrix}}}$

${\displaystyle v_{s}(t)={\frac {dx_{s}(t)}{dt}},}$
${\displaystyle r_{s}(t)={\sqrt {(x-x_{s}(t))^{2}+y^{2}+z^{2}}}}$

${\displaystyle f(r_{s})={\frac {\tanh(\sigma (r_{s}+R))-\tanh(\sigma (r_{s}-R))}{2\tanh(\sigma R)}}}$

${\displaystyle R>0\,}$${\displaystyle \sigma >0\,}$为任意参数。

阿库别瑞之后的发展

• Chris Van Den Broeck于一篇1999年的论文试图阐述一些可能的课题，亦发表在《经典和量子引力》期刊。借由将引擎运送的“曲速泡”的3+1维表面积收缩，同时扩张所包含的内部3维体积，Van Den Broeck能将运输几颗小原子所需的总能量减少到少于3个太阳质量。随后，透过对Van Den Broeck度规稍微修改，Sergey Krasnikov可以将负能量总需求缩减到几个毫克[9]
• González-Díaz的工作解决了二维量子不稳定性的问题。González-Díaz将结果发表在《物理评论D》62卷（Physical Review D Vol. 62），提议考虑封闭类时曲线的课题。这样的改善允许了多连通空间（multiply-connected spaces），结束了短程线不完备性并满足了量子不稳定性的要求。

注释

1. Alcubierre, Miguel. The warp drive: hyper-fast travel within general relativity. Classical and Quantum Gravity. 1994, 11 (5): L73–L77. Bibcode:1994CQGra..11L..73A. arXiv:gr-qc/0009013. doi:10.1088/0264-9381/11/5/001.
2. ^ Thorne, Kip; Michael Morris; Ulvi Yurtsever. Wormholes, Time Machines, and the Weak Energy Condition (PDF). Physical Review Letters. 1988, 61 (13): 1446–1449. Bibcode:1988PhRvL..61.1446M. PMID 10038800. doi:10.1103/PhysRevLett.61.1446.
3. ^ See The Alcubierre Warp Drive by John G. Cramer, where Cramer notes that "Alcubierre, following the lead of wormhole theorists, argues that quantum field theory permits the existence of regions of negative energy density under special circumstances, and cites the Casimir effect as an example."
4. ^ Roundup (PDF). Lyndon B. Johnson Space Center. July 2012 [1 October 2013].
5. ^ Dr. Harold "Sonny" White. Warp Field Mechanics 101 (PDF). NASA Johnson Space Center. 30 September 2011 [28 January 2013].
6. ^ Moskowitz, Clara. Warp Drive May Be More Feasible Than Thought, Scientists Say. Space.com. 17 September 2012 [10 January 2013].
7. ^ [1]
8. ^ 星际奇旅设定中，关于曲速引擎会运用到的“子空间/在科幻上”则与阿库别瑞所提到的重力及空间扭曲无甚关连。
9. ^ [2]

文献

• 原始论文：米给尔·阿库别瑞(Alcubierre, Miguel). The Warp Drive: Hyper-Fast Travel Within General Relativity. Class. Quantum Grav. 1994年, 11: L73–L77. eprint
• Medium review introduction article： [3]
• 罗伯·洛(Low, Robert). Speed Limits in General Relativity. Class. Quantum Grav. 1999年, 16: 543–549. eprint