Timeline for How to add Newton's constant to the metric function?

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Jul 8, 2023 at 13:21	comment	added	Saber		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
Jul 3, 2023 at 14:36	comment	added	Thomas Fritsch		@Saber This article seems to use so-called natural units all over the place, i.e. $G=1$ and $c=1$. For example in equation (5) $G_{\mu\nu}+\Lambda g_{\mu\nu}=8\pi T_{\mu\nu}$, which actually is meant to be $G_{\mu\nu}+\Lambda g_{\mu\nu}=\frac{8\pi G}{c^4} T_{\mu\nu}$. So you need to add the missing factors of $G$ and $c$ in many places to make them dimensionally consistent.
Jul 3, 2023 at 13:01	comment	added	Saber		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?
Jul 2, 2023 at 22:47	history	edited	Thomas Fritsch	CC BY-SA 4.0	added 159 characters in body
Jul 2, 2023 at 22:25	history	answered	Thomas Fritsch	CC BY-SA 4.0