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  2. Einstein–Hilbert action - Wikipedia

    en.wikipedia.org/wiki/EinsteinHilbert_action

    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]

  3. Action (physics) - Wikipedia

    en.wikipedia.org/wiki/Action_(physics)

    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.

  4. Einstein field equations - Wikipedia

    en.wikipedia.org/wiki/Einstein_field_equations

    The Einstein field equations (EFE) may be written in the form: [5] [1] + = EFE on the wall of the Rijksmuseum Boerhaave in Leiden, Netherlands. where is the Einstein tensor, is the metric tensor, is the stress–energy tensor, is the cosmological constant and is the Einstein gravitational constant.

  5. Action principles - Wikipedia

    en.wikipedia.org/wiki/Action_principles

    Inspired by Einstein's work on general relativity, the renowned mathematician David Hilbert applied the principle of least action to derive the field equations of general relativity. [25]: 186 His action, now known as the Einstein–Hilbert action, =,

  6. Tetradic Palatini action - Wikipedia

    en.wikipedia.org/wiki/Tetradic_Palatini_action

    The Einstein–Hilbert action for general relativity was first formulated purely in terms of the space-time metric. To take the metric and affine connection as independent variables in the action principle was first considered by Palatini. [1]

  7. Mathematics of general relativity - Wikipedia

    en.wikipedia.org/wiki/Mathematics_of_general...

    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.

  8. Lagrangian (field theory) - Wikipedia

    en.wikipedia.org/wiki/Lagrangian_(field_theory)

    The integral of is known as the Einstein–Hilbert action. The Riemann tensor is the tidal force tensor, and is constructed out of Christoffel symbols and derivatives of Christoffel symbols, which define the metric connection on spacetime. The gravitational field itself was historically ascribed to the metric tensor; the modern view is that the ...

  9. Alternatives to general relativity - Wikipedia

    en.wikipedia.org/wiki/Alternatives_to_general...

    For comparison with alternatives, the formulas of General Relativity [4] [5] are: = = = which can also be written = (). The Einstein–Hilbert action for general relativity is: