{"title":"近距离观察纳塔里奥的零膨胀翘曲驱动器","authors":"José Rodal","doi":"10.1007/s10773-024-05700-0","DOIUrl":null,"url":null,"abstract":"<p>We conduct a detailed analysis of Natário’s “zero-expansion” warp drive spacetime, focusing on scalar curvature invariants within the 3<span>\\(+\\)</span>1 formalism. This paper has four primary objectives: First, we establish the Petrov type classification of Natário’s spacetime, which has not been previously determined in the literature. We prove that Natário’s spacetime is Petrov type I, not fitting the Class <i>B</i> warped product spacetime definition. Second, we assess the relative magnitude of the Weyl scalar curvature invariant and compare it with the amplitudes of Einstein’s scalar and the Ricci quadratic and cubic invariants within the warp-bubble zone. Previous studies have focused on Ricci curvature and the energy-momentum tensor, neglecting the Weyl curvature, which we demonstrate plays a significant role due to the sharp localization of the form function near the warp-bubble radius. Third, we visualize several curvature invariants for Natário’s warp drive, as well as momentum density, which we show as the critical physical quantity governing the orientation of the warp drive trajectory, overshadowing space volume changes. Fourth, we critically examine claims that Natário’s warp drive is more realistic than Alcubierre’s. We demonstrate that Natário’s spacetime exhibits curvature invariant amplitudes 35 times greater than Alcubierre’s, given identical warp-bubble parameters, making Natário’s concept even less viable. Additionally, we address Mattingly et al.’s analysis, highlighting their underestimation of curvature invariant amplitudes by 21 orders of magnitude.</p>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Closer Look at Natário’s Zero-Expansion Warp Drive\",\"authors\":\"José Rodal\",\"doi\":\"10.1007/s10773-024-05700-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We conduct a detailed analysis of Natário’s “zero-expansion” warp drive spacetime, focusing on scalar curvature invariants within the 3<span>\\\\(+\\\\)</span>1 formalism. This paper has four primary objectives: First, we establish the Petrov type classification of Natário’s spacetime, which has not been previously determined in the literature. We prove that Natário’s spacetime is Petrov type I, not fitting the Class <i>B</i> warped product spacetime definition. Second, we assess the relative magnitude of the Weyl scalar curvature invariant and compare it with the amplitudes of Einstein’s scalar and the Ricci quadratic and cubic invariants within the warp-bubble zone. Previous studies have focused on Ricci curvature and the energy-momentum tensor, neglecting the Weyl curvature, which we demonstrate plays a significant role due to the sharp localization of the form function near the warp-bubble radius. Third, we visualize several curvature invariants for Natário’s warp drive, as well as momentum density, which we show as the critical physical quantity governing the orientation of the warp drive trajectory, overshadowing space volume changes. Fourth, we critically examine claims that Natário’s warp drive is more realistic than Alcubierre’s. We demonstrate that Natário’s spacetime exhibits curvature invariant amplitudes 35 times greater than Alcubierre’s, given identical warp-bubble parameters, making Natário’s concept even less viable. Additionally, we address Mattingly et al.’s analysis, highlighting their underestimation of curvature invariant amplitudes by 21 orders of magnitude.</p>\",\"PeriodicalId\":597,\"journal\":{\"name\":\"International Journal of Theoretical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-07-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Theoretical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s10773-024-05700-0\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Theoretical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s10773-024-05700-0","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
我们对纳塔莉奥的 "零膨胀 "曲速时空进行了详细分析,重点是 3\(+\)1 形式主义中的标量曲率不变式。本文有四个主要目标:首先,我们建立了纳塔里奥时空的彼得罗夫类型分类,这在之前的文献中尚未确定。我们证明纳塔里奥时空属于彼得罗夫 I 型,不符合 B 类扭曲乘积时空的定义。其次,我们评估了韦尔标量曲率不变量的相对大小,并将其与翘曲泡区内的爱因斯坦标量、利玛窦二次不变量和三次不变量的振幅进行了比较。以前的研究主要集中在利玛窦曲率和能动张量上,忽略了韦尔曲率,而我们的研究表明,由于形式函数在翘曲气泡半径附近的急剧局部化,韦尔曲率发挥了重要作用。第三,我们直观地展示了纳塔里奥翘曲驱动的几个曲率不变量,以及动量密度,我们证明动量密度是支配翘曲驱动轨迹方向的关键物理量,其重要性超过了空间体积的变化。第四,我们对有关纳塔里奥的曲速驱动比阿尔库比埃尔的曲速驱动更逼真的说法进行了批判性研究。我们证明,在翘曲气泡参数完全相同的情况下,纳塔里奥的时空表现出的曲率不变振幅比阿尔库比耶尔的大 35 倍,这使得纳塔里奥的概念更不可行。此外,我们还讨论了 Mattingly 等人的分析,强调他们低估了曲率不变振幅 21 个数量级。
A Closer Look at Natário’s Zero-Expansion Warp Drive
We conduct a detailed analysis of Natário’s “zero-expansion” warp drive spacetime, focusing on scalar curvature invariants within the 3\(+\)1 formalism. This paper has four primary objectives: First, we establish the Petrov type classification of Natário’s spacetime, which has not been previously determined in the literature. We prove that Natário’s spacetime is Petrov type I, not fitting the Class B warped product spacetime definition. Second, we assess the relative magnitude of the Weyl scalar curvature invariant and compare it with the amplitudes of Einstein’s scalar and the Ricci quadratic and cubic invariants within the warp-bubble zone. Previous studies have focused on Ricci curvature and the energy-momentum tensor, neglecting the Weyl curvature, which we demonstrate plays a significant role due to the sharp localization of the form function near the warp-bubble radius. Third, we visualize several curvature invariants for Natário’s warp drive, as well as momentum density, which we show as the critical physical quantity governing the orientation of the warp drive trajectory, overshadowing space volume changes. Fourth, we critically examine claims that Natário’s warp drive is more realistic than Alcubierre’s. We demonstrate that Natário’s spacetime exhibits curvature invariant amplitudes 35 times greater than Alcubierre’s, given identical warp-bubble parameters, making Natário’s concept even less viable. Additionally, we address Mattingly et al.’s analysis, highlighting their underestimation of curvature invariant amplitudes by 21 orders of magnitude.
期刊介绍:
International Journal of Theoretical Physics publishes original research and reviews in theoretical physics and neighboring fields. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory,as used in particle physics, and by fresh inquiry into quantum measurement theory, and other similarly fundamental areas, e.g. quantum geometry and quantum logic, etc.