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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.

他构建了一个对称teleparalline重力构造与非零非度量张量，而扭转和曲率都消失。在这个框架内，他发现精确标化球对称静态解决方案的标量张量理论建立了一个非最小耦合之间的nonmetricity标量和标量场。事实证明，Bocharova-Bronnikov-Melnikov-Bekenstein解决方案有一个对称的远程平行模拟（除了最近发现的度量远程平行模拟），而其他一些这些解决方案描述的标量黑洞配置是未知的黎曼或度量远程平行标量张量的情况下。为了帮助分析，他还推导出无毛定理的理论。我们制定了一个类似版本的Horndeski重力在一个对称telepallel几何假设，这两个曲率（一般）和扭转是零和重力只涉及到nonmetricity。我们的设置要求Euler-Lagrange方程不仅度量和标量场，而且连接应该是最多二阶。我们发现，该理论总是可以重铸为一个总和的黎曼Horndeski理论和新的条款，是纯粹的teleparallel。由于非度规性的性质，有更多可能的方法来构建二阶引力理论。在这方面，在一定的假设下，我们找到了对称遥平行Horndeski引力的最一般的k-本质扩展。