[help]how to obtain gravity eqution from gravity field Action S?

zhushualbert

could you please tell me how to obtain gravity eqution from gravity field Action S as in detail as possible, especially the derivation of calculus of variations?
or you could point out some papers for me,
and thanks very very very very very very very very very much!
p.s. as in detail as possible! thanks!

George Jones

For a careful treatment, see Chapter 4, Lagrangian and Hamiltonian formulations of general relativity, of the book A Relativist's Toolkit by Eric Poisson.

atyy

http://www.physics.uoguelph.ca/poisson/research/agr.pdf

zhushualbert

Thanks so much!

learning!