论文标题
建造一个共同平坦的标量场模型
Constructing a family of conformally flat scalar field models
论文作者
论文摘要
使用纯粹的几何方法，我们提出了一种在球形对称背景下求解运动标量场方程（非最小程度与重力）的机制。我们发现，可以完全确定\ emph {完整}的空间，该空间是petrov型O（固定平面），并且可以完全确定\ emph {渐变}保形矢量场。结果表明，整个标量字段方程还原为\ emph {single}方程，仅取决于距离$ w = r^{2} -t^{2} $离开度量函数（等效地等于标量场或电位的功能形式）。根据度量的结构或潜在的$ V $（作为$ ϕ $的函数），可以通过分析或通过数值集成找到解决方案。我们提供身体上合理的例子，并证明（反） - 保姆适合此方案。我们还重建了最近发现的解决方案\ cite {strumia：2022Kez}，该解决方案代表具有奇异性的标量膨胀气泡，并与称为Anti-De Sitter Crunch的标准气泡。
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 $ϕ$) 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.
