With respect to the above arXiv, we have parameters with dimensions as follows, $$[r] = L$$ $$[m] = L^{-1}$$ $$[e] = [C] = 1$$ $$[b] = L$$ $$[c_0] = L$$ $$[c_1] = [c_2] = [c_3] = 1$$ The $[G]$ for this 5d black brane has, $$[G] = L^3$$ So we need to add one term such as $G^{2/3}$ in the third term to solve the dimension problem with added Newton constant is this true? I didn't see in the other papers such as $G^{2/3}$ in the metric function

Thank you very much for the clear and detailed explanations. I tried to apply such a process to equation (14) from (arxiv.org/pdf/1810.09242.pdf), but I encountered some problems. Do you think this equation has a dimensional problem? How can we add this parameter without causing dimensional problems?

Thanks, but I want a non-mathematical definition of it. What does it mean to say 50 or 60 e-folds? without an equation?