伪复广义相对论有效真空部分的本构几何
Constitutive Geometry of the Effective Vacuum Sector of Pseudo-Complex General Relativity
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中文总结 AI 辅助
研究伪复广义相对论中有效真空的本构结构，将有效真空张量分解为各向同性与横向贡献，确定对数横向面积应变是最小标量本构坐标。
中文摘要 AI 辅助
在修正引力理论中，有效真空部分常由各向异性应力-能量张量描述，即便其源是几何的而非物质的，这引发了一个更广泛的问题：能否通过协变本构结构内在地刻画这类有效应力，而非将其作为奇异流体进行唯象建模？我们在伪复广义相对论（pcGR）中研究该问题，其中约束变分公式将有效真空源识别为几何起源，但未唯一确定对应的几何约束部分。对于静态伪复史瓦西解，我们证明有效真空张量可自然分解为各向异性贡献，以及与类时和径向方向正交的二维子空间内在几何相关的纯横向贡献。该分解导出了基于横向度规的本构公式，其无穷小变形可唯一分解为迹和无迹剪切模式，静态解仅具有各向同性横向响应。在依赖于横向度规代数的局域本构变量类中，其一阶变分生成具有与状态无关归一化的迹投影子，对数横向面积应变是最小标量本构坐标。
英文摘要
Effective vacuum sectors in modified theories of gravity are often represented by anisotropic stress-energy tensors, even when the underlying source is geometric rather than material. This raises a broader question: can such effective stresses be characterized intrinsically through a covariant constitutive structure, rather than modeled phenomenologically as exotic fluids? We address this question in pseudo-complex general relativity (pcGR), where a constrained variational formulation identifies the effective vacuum source as geometric in origin but does not uniquely determine the corresponding geometric constraint sector. For the static pseudo-complex Schwarzschild solution, we show that the effective vacuum tensor separates naturally into an isotropic contribution and a purely transverse contribution associated with the intrinsic geometry of the two-dimensional subspace orthogonal to the timelike and radial directions. This decomposition leads to a constitutive formulation based on the transverse metric. Its infinitesimal deformations split uniquely into trace and traceless shear modes, with the static solution having only an isotropic transverse response. Within the class of local constitutive variables that depend algebraically on the transverse metric and whose first variation generates the trace projector with stateindependent normalization, the logarithmic transverse area strain is the minimal scalar constitutive coordinate.
发表机构
- San Diego State University（圣地亚哥州立大学）
- University of California San Diego（加州大学圣地亚哥分校）
- Universidad Nacional Autónoma de México（墨西哥国立自治大学）
- Frankfurt Institute for Advanced Studies (FIAS)（法兰克福高等研究所）
- J.W. von Goethe Universität（约翰·沃尔夫冈·冯·歌德大学）
- International Center for Relativistic Astrophysics Network (ICRANet)（国际相对论天体物理中心网络）
- Universidade Federal do Rio Grande do Sul（南里奥格兰德联邦大学）
机构由 AI 辅助整理，请以论文原文为准。
