arXiv 2505.203312025-05gr-qchep-th

非最小耦合$f({\u0001},{\frak T})$引力中的稳定孤子暗物质虫洞

Stable soliton dark matter wormhole in non-minimally coupled $f({\cal Q},{\cal T})$ gravity

G. G. L. Nashed, Waleed El Hanafy

备注：: 23 pages, 12 figures, will appear in JCAP
发表信息：: JCAP 09 (2025) 040
DOI：: 10.1088/1475-7516/2025/09/040

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AI总结：

本研究在非最小耦合$f({\u0001},{\frak T})$引力框架下，基于孤子核与NFW暗物质密度分布构建可穿越虫洞解，发现大负耦合参数下无需奇异物质且虫洞动力学稳定。

摘要：

我们研究表明，物质与几何之间的非最小耦合确实有助于在特定条件下构建无需奇异物质的稳定可穿越虫洞（WHs）。在$f({\u0001},{\frak T})={\u0001}+β{\frak T}$引力这类模型中，${\u0001}$为非度规性标量，${\frak T}$为能量-动量张量的迹，物质与几何的耦合通过参数$β$引入了额外的自由度。这些自由度可模拟奇异物质的效应，甚至在特定参数选择下完全替代奇异物质。本研究的分析过程基于两种暗物质（DM）密度分布推导虫洞形状函数：一是暗物质晕中心的孤子核，二是遵循冷暗物质（CDM）通用Navarro-Frenk-White（NFW）密度分布的外晕。在这些模型中推导得到的虫洞解满足 flare-out 条件（可穿越性的必要条件）和渐近平直条件等重要几何条件。当耦合参数取较大正值时，虫洞喉处可满足零能量条件（NEC），即无需奇异物质，但此时虫洞不再是洛伦兹型的，且flare-out条件被破坏。而当耦合参数取较大负值时，只要耦合强度保持在特定范围内，就能满足零能量条件，得到无需奇异物质的合理虫洞；在后一种情况中，零能量条件仅在等效层面被破坏。我们通过包含物质-几何非最小耦合带来的新作用力的修正版Tolman-Oppenheimer-Volkoff（TOV）方程，研究了所得虫洞解的稳定性，结果表明这类虫洞可以是动力学稳定的。

英文摘要：

We show that non-minimal coupling between matter and geometry can indeed help in constructing stable, traversable, wormholes (WHs) without requiring exotic matter under certain conditions. In models like $f({\cal Q},{\cal T})={\cal Q}+β{\cal T}$ gravity, where ${\cal Q}$ is the non-metricity scalar, and ${\cal T}$ is the trace of the energy-momentum tensor, the coupling between matter and geometry introduces additional degrees of freedom in terms of the parameter $β$. These can mimic the effects of exotic matter or even replace it entirely under specific parameter choice. The analysis involves deriving WH shape functions based on two dark matter (DM) density profiles: a solitonic core at the center of DM halos, and the outer halo follows the universal Navarro-Frenk-White (NFW) density profile of cold DM (CDM). The wormhole solutions derived in these models satisfy important geometric conditions like: Flaring-out condition (necessary for traversability) and asymptotic flatness condition. For large positive coupling parameter, the null energy condition (NEC) can be satisfied at the wormhole throat, meaning exotic matter is not needed, while the wormhole is no longer Lorentzian and the flaring-out condition is broken. However, for large negative coupling parameter, the NEC can be satisfied, allowing for healthy wormholes without exotic matter, provided the coupling strength remains within certain bounds. In the latter case, the NEC is broken only effectively. We investigate the stability of the obtained wormhole solutions by virtue of a modified version of Tolman-Oppenheimer-Volkoff (TOV) equation, which includes a new force due to matter-geometry non-minimal, showing that these wormholes can be dynamically stable.

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