Einstein–Hilbert action

The Einstein - Hilbert action is a mathematical expression of the general theory of relativity.

From these effects, Einstein's field equations can be derived using the principle of least action. It was first stated by David Hilbert.

Here, the metric tensor of the Krümmungsskalar, the speed of light and the Newtonian gravitational constant.

The requirement that the variation of the effect of any variation of the metric disappears, returns the equations

Where the components of the Ricci tensor respectively.

These are the field equations in vacuum in the absence of particles and fields and at zero vacuum energy density. The right side of the field equations, the components of the energy-momentum tensor obtained by varying the part of the effect, which describes the subject matter, according to the metric. The prefactor

Prior to the Einstein - Hilbert action determines the strength, generate gravity with the energy and momentum.

To obtain the cosmological constant in the field equations, one can effect a term

To add. Such a term can also be interpreted as a proportion of the energy-momentum tensor, which has the advantage that it provides a physical justification for the cosmological constant. There are now (2013 ) a variety of models with various degrees of success try a cosmological constant through the material content of the universe to explain.

• General Theory of Relativity