The Duality of Time Theory

In 1915, when Hilbert applied the principle of least action, that we described in chapter II (section 15), on General Relativity, Einstein’s Field equations were obtained, as described below. This action is therefore called the Einstein-Hilbert action. With themetric signature, the gravitational part of the action is given as:

whereis the determinant of the metric tensor matrix,is the Ricci scalar,is Einstein’s constant,is the gravitational constant andis the speed of light in vacuum.

The integral is taken over the whole space-time if it converges, but if it does not converge,is no longer well-defined, but a modified definition where one integrates over arbitrarily large, relatively compact domains, still yields the Einstein equation as the Euler-Lagrange equation of the Einstein-Hilbert action.