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For the second step see the article about the Einstein-Hilbert action.
The field equations may be derived by using the Einstein-Hilbert action.
The other term is the equivalent of the Einstein-Hilbert action, as extended to all 5 dimensions.
This used the functional now called the Einstein-Hilbert action.
This would eliminate the constant c/(16πG) from the Einstein-Hilbert action.
For the Lagrangian of gravity in general relativity, see Einstein-Hilbert action.
See Einstein-Hilbert action for more information.
The Einstein equation also involves a variational principle, the Einstein-Hilbert action.
The Einstein-Hilbert action for general relativity was first formulated purely in terms of the space-time metric.
This is the Lagrangian from the Einstein-Hilbert action.
The Einstein-Hilbert action is the basis for the most elementary variational principle from which the field equations of general relativity can be defined.
This gives rise to an effective action which to one-loop order contains the Einstein-Hilbert action with a cosmological constant.
In general relativity, the scalar curvature is the Lagrangian density for the Einstein-Hilbert action.
Hilbert was the first to correctly state the Einstein-Hilbert action for GR, which is:
The field equations are derived by postulating the Einstein-Hilbert action governs the evolution of the gauge fields, i.e.
Here we see that the differential form language leads to an equivalent action to that of the normal Einstein-Hilbert action, using the relations and .
(also see Cosmological constant, Einstein-Hilbert action, Quintessence (physics))
This is to be contrasted with the usual Einstein-Hilbert action where the Lagrangian is just the Ricci scalar.
The model assumes an action consisting of two terms: One term is the usual Einstein-Hilbert action, which involves only the 4-D spacetime dimensions.
In f(R) gravity, one seeks to generalise the Lagrangian of the Einstein-Hilbert action:
The action in structural quantum gravity can be subdivided into the action of classical general relativity (called Einstein-Hilbert action) and a quantum correction.
The coupling constant is usually represented by (Xi), which features in the action (constructed by modifying the Einstein-Hilbert action):
A discrete version of the Einstein-Hilbert action is obtained by considering so-called deficit angles of these blocks, a zero deficit angle corresponding to no curvature.
Such an axiom might establish a sheaf structure that supports uniform mapping of Einstein-Hilbert actions and Feynman actions across alternate universes.
This would eliminate 8πG from the Einstein field equations, Einstein-Hilbert action, Friedmann equations, and the Poisson equation for gravitation.