带有宇宙学常数的一般D型爱因斯坦-麦克斯韦解在$\boldsymbol{\text{mathscr{J}}}$处的引力辐射研究
Study of gravitational radiation at $\mathscr{J}$ for the general type-D Einstein-Maxwell solution with cosmological constant
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中文总结 AI 辅助
该研究针对带任意符号宇宙学常数的一般D型爱因斯坦-麦克斯韦解，表征其引力辐射特征，明确辐射逃逸条件，计算相关张量并重铸度量参数化形式，探究对称轴、亏角与辐射的关系。
中文摘要 AI 辅助
我们表征了带有任意符号宇宙学常数$\boldsymbol{\text{Λ}}$的一般普莱班斯基-杰米亚斯基（Plebański-Demiański）D型解中存在的引力辐射。我们证明，辐射逃逸至无穷远当且仅当加速度参数非零。我们计算了负$\boldsymbol{\text{Λ}}$下的科顿-约克（Cotton-York）张量和无穷远处的边界应力-能量张量，以及正$\boldsymbol{\text{Λ}}$下用于补充$\boldsymbol{\text{mathscr{J}}}$处初始或最终数据的D张量。此外，我们通过简单的同形变换将该度量族的近期参数化重铸为新形式，正确确定$\boldsymbol{\text{Λ}}$，并研究可能的对称轴的存在性与正则性，探究亏角与辐射之间的关系。
英文摘要
We characterize the gravitational radiation present in the general Plebański-Demiański type~D solution with cosmological constant $Λ$ of any sign. We show that radiation escapes towards infinity if and only if the acceleration parameter is non-zero. We calculate the Cotton-York tensor and the boundary stress-energy tensor at infinity for negative $Λ$, and for positive $Λ$ the $D$ tensor that complements initial or final data at $\mathscr{J}$. In addition, we recast a recent parametrization of this family of metrics into a new form by a simple homothety, correctly identifying $Λ$, and study the existence and regularity of the possible axes of symmetry, searching for a relation between deficit angles and radiation. We also identify the branch of general non-radiating solutions with non-vanishing Cotton-York tensor at $ \mathscr{J} $.
发表机构
- Universidad del País Vasco UPV/EHU（巴斯克大学）
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