多方程虫洞
Polytropic wormholes
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中文总结 AI 辅助
该研究针对广义相对论中可穿越虫洞需非标准物质源的问题，在统一框架内研究多方程虫洞，推导均匀与非均匀构型的解，建立多方程物质与虫洞几何的联系，为构造紧凑虫洞提供灵活框架。
中文摘要 AI 辅助
广义相对论中的可穿越虫洞需要非标准物质源，因此识别具有物理动机的状态方程尤为重要。我们研究由多方程状态方程支撑的虫洞，在统一框架内考虑均匀和非均匀构型，推导相应的解并分析多方程参数对几何和能量条件的影响。在均匀情形下，多方程构造产生一致的虫洞内部，其几何和物质内容由常数多方程参数支配；在非均匀情形下，我们得到一个通用解析表达式，表明几何完全由径向多方程系数ω(r)决定。对于正的ω(r)，物理上有意义的解的要求自然将多方程指数限制为奇整数。我们利用幂律轮廓构造了显式的解类，展现出不同的参数 regime 和有限的径向支撑。有趣的是，当指数α=2γ-3时，会自然出现一种广义的“荒谬良性”可穿越虫洞状构型。尽管 flare-out 条件意味着喉部处的零能量条件被违反，但非均匀框架允许对其径向分布进行控制。我们的结果建立了多方程物质与虫洞几何之间的系统联系，为构造具有局域奇异物质的紧凑虫洞提供了灵活框架。
英文摘要
Traversable wormholes in general relativity require non-standard matter sources, making the identification of physically motivated equations of state particularly important. We investigate wormholes supported by a polytropic equation of state, considering homogeneous and inhomogeneous configurations within a unified framework. We derive the corresponding solutions and analyze the effects of the polytropic parameters on the geometry and energy conditions. In the homogeneous case, the polytropic construction yields a consistent wormhole interior whose geometry and matter content are governed by the constant polytropic parameters. For the inhomogeneous case, we obtain a general analytical expression showing that the geometry is completely determined by the radial polytropic coefficient $ω(r)$. For positive $ω(r)$, the requirement for physically meaningful solutions naturally restricts the polytropic exponent to odd integer values. Using a power-law profile, we construct explicit classes of solutions exhibiting distinct parameter regimes and finite radial support. Interestingly enough, for an exponent $α=2γ-3$, a generalized absurdly benign traversable wormhole-like configuration emerges naturally. Although the flare-out condition implies null-energy-condition violation at the throat, the inhomogeneous framework allows its radial distribution to be controlled. Our results establish a systematic connection between polytropic matter and wormhole geometry, providing a flexible framework for constructing compact wormholes with localized exotic matter.
发表机构
- Università degli Studi di Bergamo（贝加莫大学）
- I.N.F.N.- sezione di Milano（意大利国家核物理研究所米兰分部）
- National Observatory of Athens（雅典国立天文台）
- Universidad Católica del Norte（北天主教学大学）
- University of Science and Technology of China（中国科学技术大学）
机构由 AI 辅助整理，请以论文原文为准。
