Constructing a family of conformally flat scalar field models
arXiv:2211.01084 · doi:10.1088/1361-6382/acbe88
Abstract
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 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 (as a function of ) 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.
8 pages, no figures, uses iop class style; (v2) minor typos corrected; (v3) small extension in the abstract to indicate the inclusion of the non-minimally coupled scalar field within the article and some new references were added. Matches version to appear in Classical and Quantum Gravity as a Letter