The discussion centers around the Einstein-Hilbert action integral, specifically the equation $$S=\int{\sqrt{g}d^4xR}$$. Participants are exploring its derivation, the mathematical principles behind it, and the uniqueness of the action in the context of general relativity.
Participants generally express uncertainty regarding the derivation and proof of the Einstein-Hilbert action, with multiple competing views on the existence and nature of such proofs. There is no consensus on a definitive derivation or understanding of the action.
Some discussions touch on the limitations of existing proofs and the need for further mathematical steps to clarify the derivation of the Einstein-Hilbert action. The conversation also highlights the complexity of the Euler-Lagrange formula when applied to second derivatives.
Ok, samalkhaitat first of all very nice post. besides I would like to express that you say that For b = 0 , the value of c can be determined by comparing the Newtonian limit of the theory with Newton’s gravity, this gives c=1/16piG. Could you show me how it is obtained ? Very thanks in advance...samalkhaiat said:Okay I included new stuff (Appendix A) in the PDF which answer the questions you put to me in PM and those you asked in this thread.
Pick up any textbook on GR and look up the Newtonian limit. All textbooks on GR do consider the Newtonian limit. By the way, have you taken academic course on General Relativity?mertcan said:the value of c can be determined by comparing the Newtonian limit of the theory with Newton’s gravity, this gives c=1/16piG. Could you show me how it is obtained ?
yes, I have taken lots of courses related to that topic, but ıt has been 2 years, now I am senior( also almost finished second university), and endeavour to remember all the stuff in order to ensure a tremendous master education. By the way I remembered the answer to my last question.:Dsamalkhaiat said:Pick up any textbook on GR and look up the Newtonian limit. All textbooks on GR do consider the Newtonian limit. By the way, have you taken academic course on General Relativity?