{"title":"用杨-米尔斯卡西米尔源生成四维虫洞","authors":"A.C.L. Santos , R.V. Maluf , C.R. Muniz","doi":"10.1016/j.aop.2024.169775","DOIUrl":null,"url":null,"abstract":"<div><p>This work presents a new static and spherically symmetric traversable wormhole solution in General Relativity, which is supported by the quantum vacuum fluctuations associated with the Casimir effect of the Yang–Mills field confined between perfect chromometallic mirrors in <span><math><mrow><mo>(</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span> dimensions, recently fitted using first-principle numerical simulations. Initially, we employ a perturbative approach for <span><math><mrow><mi>x</mi><mo>=</mo><mi>m</mi><mi>r</mi><mo>≪</mo><mn>1</mn></mrow></math></span>, where <span><math><mi>m</mi></math></span> represents the Casimir mass and <span><math><mi>r</mi></math></span> is the radial coordinate. This approach has proven to be a reasonable approximation when compared with the exact case in this regime. To find well-behaved redshift functions, we impose constraints on the free parameters. As expected, this solution recovers the electromagnetic-like Casimir solution for <span><math><mrow><mi>m</mi><mo>=</mo><mn>0</mn></mrow></math></span>. Analyzing the traversability conditions, we graphically find that all are satisfied for <span><math><mrow><mn>0</mn><mo>≤</mo><mi>m</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>17</mn></mrow></math></span>. On the other hand, all the energy conditions are violated, as usual in this context due to the quantum origin of the source. Stability from Tolman–Oppenheimer–Volkov (TOV) equation is guaranteed for all <span><math><mi>r</mi></math></span> and from the speed of sound for <span><math><mrow><mn>0</mn><mo>.</mo><mn>16</mn><mo>≤</mo><mi>m</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>18</mn></mrow></math></span>. Therefore, for <span><math><mrow><mn>0</mn><mo>.</mo><mn>16</mn><mo>≤</mo><mi>m</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>17</mn></mrow></math></span>, we will have a stable solution that satisfies all traversability conditions.</p></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"469 ","pages":"Article 169775"},"PeriodicalIF":3.0000,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generating 4-dimensional wormholes with Yang–Mills Casimir sources\",\"authors\":\"A.C.L. Santos , R.V. Maluf , C.R. Muniz\",\"doi\":\"10.1016/j.aop.2024.169775\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This work presents a new static and spherically symmetric traversable wormhole solution in General Relativity, which is supported by the quantum vacuum fluctuations associated with the Casimir effect of the Yang–Mills field confined between perfect chromometallic mirrors in <span><math><mrow><mo>(</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span> dimensions, recently fitted using first-principle numerical simulations. Initially, we employ a perturbative approach for <span><math><mrow><mi>x</mi><mo>=</mo><mi>m</mi><mi>r</mi><mo>≪</mo><mn>1</mn></mrow></math></span>, where <span><math><mi>m</mi></math></span> represents the Casimir mass and <span><math><mi>r</mi></math></span> is the radial coordinate. This approach has proven to be a reasonable approximation when compared with the exact case in this regime. To find well-behaved redshift functions, we impose constraints on the free parameters. As expected, this solution recovers the electromagnetic-like Casimir solution for <span><math><mrow><mi>m</mi><mo>=</mo><mn>0</mn></mrow></math></span>. Analyzing the traversability conditions, we graphically find that all are satisfied for <span><math><mrow><mn>0</mn><mo>≤</mo><mi>m</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>17</mn></mrow></math></span>. On the other hand, all the energy conditions are violated, as usual in this context due to the quantum origin of the source. Stability from Tolman–Oppenheimer–Volkov (TOV) equation is guaranteed for all <span><math><mi>r</mi></math></span> and from the speed of sound for <span><math><mrow><mn>0</mn><mo>.</mo><mn>16</mn><mo>≤</mo><mi>m</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>18</mn></mrow></math></span>. Therefore, for <span><math><mrow><mn>0</mn><mo>.</mo><mn>16</mn><mo>≤</mo><mi>m</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>17</mn></mrow></math></span>, we will have a stable solution that satisfies all traversability conditions.</p></div>\",\"PeriodicalId\":8249,\"journal\":{\"name\":\"Annals of Physics\",\"volume\":\"469 \",\"pages\":\"Article 169775\"},\"PeriodicalIF\":3.0000,\"publicationDate\":\"2024-08-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0003491624001829\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0003491624001829","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
本研究提出了广义相对论中一种新的静态球对称可穿越虫洞方案,该方案得到了量子真空波动的支持,而量子真空波动与限制在(3+1)维完美铬金属镜面之间的杨-米尔斯场的卡西米尔效应有关。最初,我们采用了 x=mr≪1 的微扰方法,其中 m 代表卡西米尔质量,r 是径向坐标。事实证明,与这一机制下的精确情况相比,这种方法是一种合理的近似方法。为了找到良好的红移函数,我们对自由参数施加了约束。分析可穿越性条件,我们发现在 0≤m≤0.17 时,所有条件都满足。另一方面,由于源的量子起源,所有的能量条件都被违反了。托尔曼-奥本海默-沃尔科夫(Tolman-Oppenheimer-Volkov,TOV)方程保证了所有 r 和 0.16≤m≤0.18 时声速的稳定性。因此,对于 0.16≤m≤0.17 时,我们将有一个满足所有可穿越条件的稳定解。
Generating 4-dimensional wormholes with Yang–Mills Casimir sources
This work presents a new static and spherically symmetric traversable wormhole solution in General Relativity, which is supported by the quantum vacuum fluctuations associated with the Casimir effect of the Yang–Mills field confined between perfect chromometallic mirrors in dimensions, recently fitted using first-principle numerical simulations. Initially, we employ a perturbative approach for , where represents the Casimir mass and is the radial coordinate. This approach has proven to be a reasonable approximation when compared with the exact case in this regime. To find well-behaved redshift functions, we impose constraints on the free parameters. As expected, this solution recovers the electromagnetic-like Casimir solution for . Analyzing the traversability conditions, we graphically find that all are satisfied for . On the other hand, all the energy conditions are violated, as usual in this context due to the quantum origin of the source. Stability from Tolman–Oppenheimer–Volkov (TOV) equation is guaranteed for all and from the speed of sound for . Therefore, for , we will have a stable solution that satisfies all traversability conditions.
期刊介绍:
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