标题： 构造一类共形平坦标量场模型 显示英文标题

标题： Constructing a family of conformally flat scalar field models

摘要： 使用纯粹的几何方法，我们提出了一种机制来求解在球对称背景下的标量场运动方程（与引力非最小耦合）。我们发现，\emph{完整}类时空，它们是Petrov类型O（共形平坦）并允许一个\emph{梯度}共形向量场，可以被完全确定。证明了标量场方程的完整群约简为一个\emph{单个}方程，该方程仅依赖于距离$w=r^{2}-t^{2}$，从而使得度规函数（等价于标量场或势能的功能形式）可以自由选择。根据度规或势能$V$的结构（作为$\phi $的函数），可以通过解析方法或数值积分找到解。我们提供了物理上合理的例子，并证明了(反)德西特符合此方案。我们还重构了一个最近发现的解\cite{Strumia:2022kez}，它代表了一个膨胀的标量泡，其度规具有奇点，对应于所谓的反德西特挤压。 显示英文摘要

摘要： Using purely geometrical methods we present a mechanism to solve the scalar field equations of motion (non-minimally coupled with gravity) in a spherically symmetric background. We found that the \emph{full }set of spacetimes, which are of Petrov type O (conformally flat) and admit a \emph{gradient} Conformal Vector Field, can be determined completely. It is shown that the full group of scalar field equations reduced to a \emph{single} equation that depends only on the distance $w=r^{2}-t^{2}$ leaving the metric function (equivalently the functional form of the scalar field or the potential) freely chosen. Depending on the structure of the metric or the potential $V$ (as a function of $\phi $) a solution can be found either analytically or via numerical integration. We provide physically sound examples and prove that (Anti)-de Sitter fits this scheme. We also reconstruct a recently found solution \cite{Strumia:2022kez} representing an expanding scalar bubble with metric that has a singularity and corresponds to what is termed as Anti-de Sitter crunch.