Field equations for hairy black holes in star trigravity

This DOI is supplementary material for our paper "Black holes in multi-metric gravity II: hairy solutions and linear stability of the non- and partially proportional branches", found at https://arxiv.org/abs/2410.10976. It includes the Mathematica notebook referred to in the paper where we reduce the field equations for the 3-metric star model we introduce in section IV down to a set of coupled first order nonlinear ODEs which one may in principle integrate. The notebook follows the prescription we outlined in section IV of the paper, and refers explicitly to the paper at various points to aid comprehension.