We generalize the algorithm that establishes the correspondence between metric-affine Eddington-inspired Born-Infeld (EiBI) gravity and General Relativity (GR) to any bosonic matter sector. Along the way, a polished version of the proof of existence of a metric compatible frame associated to any metric-affine Ricci-Based Gravity (RBG) is presented. Particular attention is given to the problem of generating solutions of a RBG from the GR counterpart, providing a general recipe for the EiBI case. This extends previous results obtained for specific matter that included anisotropic fluids, scalar fields and electromagnetic fields.

中文翻译：

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从广义相对论生成基于 Ricci 的引力理论的解决方案

我们将建立度量仿射 Eddington 启发的 Born-Infeld (EiBI) 引力和广义相对论 (GR) 之间对应关系的算法推广到任何玻色子物质扇区。在此过程中，提出了与任何度量仿射 Ricci-Based Gravity (RBG) 相关联的度量兼容框架的存在证明的完善版本。特别关注从 GR 对应物生成 RBG 解决方案的问题，为 EiBI 案例提供了一般配方。这扩展了先前针对特定物质获得的结果，包括各向异性流体、标量场和电磁场。