爱因斯坦-狄拉克理论中可穿越虫洞的阻碍
Obstructions to Traversable Wormholes in Einstein-Dirac Theory
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中文总结 AI 辅助
本文研究爱因斯坦-狄拉克理论中可穿越虫洞的存在性，发现虽狄拉克场可违反平均零能条件，但数值搜寻未找到满足要求的完整可穿越虫洞解，表明该系统无此类解。
中文摘要 AI 辅助
可穿越虫洞是广义相对论最引人注目的假想解之一，但这类几何均需要违反平均零能条件（ANEC）的物质，狄拉克场是这类物质的可能候选。近期多项研究声称找到了经典爱因斯坦-狄拉克-麦克斯韦系统的可穿越虫洞解，但这些研究未恰当考虑单粒子态无电磁自相互作用，且其模函数为正频率。本文中，我们证明在某些固定虫洞几何上的经典正频率狄拉克场可违反ANEC，因此确实是可穿越虫洞的源候选。随后我们数值搜寻由确定频率ω>0、角动量量子数ℓ和确定宇称的狄拉克场源产生的静态、球对称、渐近平直可穿越虫洞几何，发现了“部分虫洞解”，其具有规则虫洞喉和虫洞一端的正确渐近行为，但这类解无法延伸至第二个渐近平直端。对于反射对称虫洞，我们额外在不假设狄拉克解具有确定宇称的情况下进行搜寻，在对形成喉的渐近数据进行广泛扫描后，发现无法得到反射对称虫洞喉所需的条件。综合这些结果，强烈支持由物理上有意义的狄拉克场源产生的爱因斯坦-狄拉克系统不存在可穿越虫洞解。
英文摘要
Traversable wormholes are among the most striking hypothetical solutions of general relativity, but every such geometry requires matter that violates the averaged null energy condition (ANEC). A possible candidate for such matter is the Dirac field. Several recent works have claimed traversable wormhole solutions of the classical Einstein-Dirac-Maxwell system, but these works did not properly take into account that single-particle states do not self-interact electromagnetically and that the mode functions of single-particle states are of positive frequency. In this paper, we show that classical, positive-frequency Dirac fields on certain fixed wormhole geometries can violate ANEC, so they are indeed candidates for sourcing traversable wormholes. We then numerically search for static, spherically symmetric, asymptotically flat traversable wormhole geometries sourced by Dirac fields of a definite frequency $ω>0$, angular momentum quantum number $\ell$, and definite parity. We find "partial-wormhole solutions," describing a regular wormhole throat with correct asymptotics at one end of the wormhole, but we find that these solutions cannot be continued to a second asymptotically flat end. In the case of reflection-symmetric wormholes, we perform an additional search where we do not assume that the Dirac solution has a definite parity. In this case, after an extensive scan of throat-forming asymptotic data, we find that the conditions necessary for a reflection-symmetric wormhole throat cannot be obtained. Taken together, these results strongly support that the Einstein-Dirac system does not admit traversable wormhole solutions when sourced by a physically meaningful Dirac field.
