arXiv 2304.044192023-04gr-qchep-th

对称远平行$f\left( Q\right)$理论中的各向异性解：Kantowski-Sachs与Bianchi III LRS宇宙学

Anisotropic Solutions in Symmetric Teleparallel $f\left( Q\right)$-theory: Kantowski-Sachs and Bianchi III LRS Cosmologies

N. Dimakis, M. Roumeliotis, A. Paliathanasis, T. Christodoulakis

备注：: 42 pages, no figures, Latex2e source file, EPJC accepted version

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AI总结：

该研究在对称远平行$f(Q)$理论框架下，针对Kantowski-Sachs和局部旋转对称Bianchi III型两类各向异性时空，推导场方程并确定了真空及含理想流体情形下支持自相似解的$f(Q)$拉格朗日量形式，还补充了静态球对称时空的相关自相似解。

摘要：

我们研究了对称远平行$f\left( Q\right)$理论中各向异性自相似精确解的存在性。背景几何方面，我们考虑Kantowski-Sachs几何与局部旋转对称的Bianchi III型几何。这两种各向异性时空具有特殊研究价值，因为在各向同性极限下，它们分别对应闭合与开放的Friedmann–Lemaître–Robertson–Walker宇宙学。每种时空都存在两类不同的、具备时空对称性的平坦对称联络。我们推导了场方程，并据此确定了能产生自相似解的$f\left( Q\right)$拉格朗日量的函数形式。我们首先考虑真空情形，随后引入理想流体形式的物质源。最后，我们还给出了若干对应静态球对称时空的自相似解。

英文摘要：

We investigate the existence of anisotropic self-similar exact solutions in symmetric teleparallel $f\left( Q\right)$-theory. For the background geometry we consider the Kantowski-Sachs and the Locally Rotationally Symmetric Bianchi type III geometries. These two anisotropic spacetimes are of special interest because in the limit of isotropy they are related to the closed and open Friedmann--Lema\^ıtre--Robertson--Walker cosmologies respectively. For each spacetime there exist two distinct families of flat, symmetric connections, which share the symmetries of the spacetime. We present the field equations, and from them, we determine the functional form of the $f\left( Q\right)$ Lagrangian which yields self-similar solutions. We initially consider the vacuum case and subsequently we introduce a matter source in terms of a perfect fluid. Last but not least, we report some self-similar solutions corresponding to static spherically symmetric spacetimes.

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