In my studies of methods to simplify the Einstein field equations, I first decided to go about expanding the Ricci tensor in terms of the metric tensor. I have been mostly successful in doing this, but there are a couple of complications that I would like your opinions on. At the bottom of this post, I will leave an attachment that leads to the word document that shows my work when expanding the Ricci tensor. In this attachment, I have highlighted two sections. Now here are my questions: 1. In my first highlighted section, is there any way to further simplify this expression for the derivative of this Christoffel symbol? Is there perhaps some property of Christoffel symbols that I can use? 2. In my second highlighted section at the bottom, how would I express the multiplication of those two Christoffel symbols without overloading any indices (especially the c index)? Can somebody please type out that expression so that I can see what I should do when multiplying two Christoffel symbol formulas? 3. Does everything else look right to you all? Is there any way to simplify any other part that I did not ask about? Here is the the attachment: View attachment typing_the_terms_of_the_ricci_tensor 2._docx.docx P.S. I would have just posted the attachment here directly on the forum, but I could not do this for some unknown reason when I clicked on the attachment button.