The Theory of General Relativity

Abstract

G L, where L is a 4-form called Lagrange density. In electrodynamics, it is given by L := − 2 dA ∧ ? dA + A ∧ J. Now consider an infinitesimal variation of the electromagnetic field byA→ A+ Q, where Q is a 1-form and where 0 < 1 is small. The principle of least action tells us that S does not change to lowest order in , provided that Q vanishes on the boundary ∂G. (a) Show that the stationarity of S leads us to the condition (2P) ∫