メトリック・アフィン重力理論における摂動論とその応用

微扰理论及其在度量仿射引力理论中的应用

基本信息

批准号：
22KF0135
负责人：
須山輝明
金额：
$ 1.47万
依托单位：
Tokyo Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for JSPS Fellows
财政年份：
2023
资助国家：
日本
起止时间：
2023-03-08 至 2024-03-31
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22KF0135/
关键词：
Gravity

项目摘要

He constructed a Symmetric teleparallel gravity constructed with a nonzero nonmetricity tensor while both torsion and curvature are vanishing. In this framework, he found exact scalarised spherically symmetric static solutions in scalar-tensor theories built with a nonminimal coupling between the nonmetricity scalar and a scalar field. It turns out that the Bocharova-Bronnikov-Melnikov-Bekenstein solution has a symmetric teleparallel analogue (in addition to the recently found metric teleparallel analogue), while some other of thesesolutions describe scalarised black hole configurations that are not known in the Riemannian or metric teleparallel scalar-tensor case. To aid the analysis he also derived no-hair theorems for the theory.We formulated an analogue version of Horndeski gravity in a symmetric teleparallel geometry which assumes that both the curvature (general) and torsion are vanishing and gravity is only related to nonmetricity. Our setup requires that the Euler-Lagrange equations for not only metric and scalar field but also connection should be at most second order. We find that the theory can be always recast as a sum of the Riemannian Horndeski theory and new terms that are purely teleparallel. Due to the nature of nonmetricity, there are many more possible ways of constructing second-order theories of gravity. In this regard, up to some assumptions, we find the most general k-essence extension of Symmetric Teleparallel Horndeski gravity.

他构建了一个用非零的非对称性张量构建的对称电触电引力，而扭转和曲率都消失了。在此框架中，他在标量调整理论中发现了确切的标量对称静态溶液，该理论构建了非对象标量和标量场之间的非微耦合。事实证明，Bocharova-Bronnikov-Melnikov-Bekenstein解决方案具有对称触发平行的类似物（除了最近发现的度量触发平行的类似物之外），而其他一些方法描述了标量的黑洞配置，在Riemannian或Metric Teleparallalleallallal scalparallalleal-Scalarelallal-censor ceas中尚不清楚。为了帮助分析，他还为该理论得出了无发的定理。我们在对称远程的几何形状中制定了Horndeski Gravity的模拟版本，该几何形状假设曲率（一般）和扭曲都消失了，并且重力仅与非量度有关。我们的设置要求不仅指标和标量字段的Euler-Lagrange方程，而且连接最多应是二阶。我们发现，该理论总是可以作为Riemannian Horndeski理论的总和，纯粹是触电的总和。由于非金属的性质，还有更多可能的方法来构建重力理论。在这方面，最终，我们发现了对称远程的Horndeski Gravity的最通用的k丝扩展。