The Einstein-Hilbert action integral, represented as $$S=\int{\sqrt{g}d^4xR}$$, is derived from principles of general relativity (GR) and is unique due to its dependence on the metric tensor and its derivatives. The Ricci scalar, ##R##, is the only scalar that can be constructed from the pseudo-metric components up to their second derivatives, leading to the formulation of the action. The discussion emphasizes the necessity of a mathematical demonstration for the derivation of this action, particularly in relation to the Lagrangian density and the Euler-Lagrange equations.
PREREQUISITESPhysicists, mathematicians, and students of general relativity seeking a deeper understanding of the Einstein-Hilbert action and its derivation.
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?