Search results
Results From The WOW.Com Content Network
The Einstein–Hilbert action in general relativity is the action that yields the Einstein field equations through the stationary-action principle. With the (− + + +) metric signature , the gravitational part of the action is given as [ 1 ]
Hilbert claimed priority for the introduction of the Riemann scalar into the action principle and the derivation of the field equations from it," [B 6] (Sauer mentions a letter and a draft letter where Hilbert defends his priority for the action functional) "and Einstein admitted publicly that Hilbert (and Lorentz) had succeeded in giving the ...
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. This novel idea finds application in approximation methods in numerical relativity and quantum gravity , the latter using a generalisation of Regge calculus.
In general relativity, the Gibbons–Hawking–York boundary term is a term that needs to be added to the Einstein–Hilbert action when the underlying spacetime manifold has a boundary. The Einstein–Hilbert action is the basis for the most elementary variational principle from which the field equations of general relativity can be defined.
The second-order formalism action is then acquired by substituting this expression for the spin connection back into the action, yielding additional quartic gravitino vertices, with the Einstein–Hilbert and Rarita–Schwinger actions now being written with a torsionless spin connection that explicitly depends on the vielbeins.
The names of action principles have evolved over time and differ in details of the endpoints of the paths and the nature of the variation. Quantum action principles generalize and justify the older classical principles. Action principles are the basis for Feynman's version of quantum mechanics, general relativity and quantum field theory.
The action principle can be extended to obtain the equations of motion for fields, such as the electromagnetic field or gravitational field. Maxwell's equations can be derived as conditions of stationary action. The Einstein equation utilizes the Einstein–Hilbert action as constrained by a variational principle.
Another important action is the Plebanski action (see the entry on the Barrett–Crane model), and proving that it gives general relativity under certain conditions involves showing it reduces to the Palatini action under these conditions. Here we present definitions and calculate Einstein's equations from the Palatini action in detail.