Editing Einstein–Hilbert action (section)

== Discussion ==
Deriving equations of motion from an action has several advantages. First, it allows for easy unification of general relativity with other classical field theories (such as [[Maxwell theory]]), which are also formulated in terms of an action. In the process, the derivation identifies a natural candidate for the source term coupling the metric to matter fields. Moreover, symmetries of the action allow for easy identification of conserved quantities through [[Noether's theorem]].

In general relativity, the action is usually assumed to be a [[functional (mathematics)|functional]] of the metric (and matter fields), and the [[connection (mathematics)|connection]] is given by the [[Levi-Civita connection]]. The [[Palatini action|Palatini formulation]] of general relativity assumes the metric and connection to be independent, and varies with respect to both independently, which makes it possible to include fermionic matter fields with non-integer spin.

The Einstein equations in the presence of matter are given by adding the matter action to the Einstein–Hilbert action.