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

他构造了一个对称的远平行引力，它由一个非零的非对称张量构成，而挠率和曲率都是零的。在这个框架中，他在标量张量理论中找到了精确的标量化球对称静态解，该理论建立在非度规标量和标量场之间的非最小耦合。结果表明，Bocharova-Bronnikov-Melnikov-Bekenstein解具有对称的远平行类比(除了最近发现的度规远平行类比)，而其他一些解描述了在黎曼或度规远平行标量张量情况下未知的标量化黑洞构型。为了辅助分析，他还推导了该理论的无毛定理。我们在对称的远平行几何中建立了Horndeski引力的模拟版本，假设曲率(一般)和挠率都为零，而重力只与非度规有关。我们的设置不仅要求度规场和标量场的欧拉-拉格朗日方程，而且要求连接的欧拉-拉格朗日方程至多为二阶。我们发现，这个理论总是可以被重塑为黎曼-霍恩德斯基理论和纯远程平行的新项的总和。由于非度规的性质，有更多可能的方法来构建二阶引力理论。在这一点上，在一定的假设下，我们得到了对称远程平行Horndeski引力的最一般的k-本质推广。

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.