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Historical question: Equations of motion from lagrangian

  1. Feb 8, 2012 #1
    Hey, in general relativity, essentially I am asking how any metric (I.e. schwarzschild metric) was found. are the metrics derived or are they extrapolated from the correct lagrange equations of motion? If there is a derivation available, please provide a link.

  2. jcsd
  3. Feb 8, 2012 #2


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    Hilbert showed how to derive the field equations for GR from a Lagrangian density. Soon after Einstein & Hilbert the first solutions have been found - but forgetting about the physicalcontent this is nothing else but solving non-linear partial differential equations; of course it can be done but there is no complete theory as for linear partial differential equations
  4. Feb 8, 2012 #3


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    The Einstein tensor comes from an action which is extremised according to the least action principle.

    The Schwarzschild metric can then be derived using nothing more than the spherical symmetry and the requirement that the Einstein tensor be zero.

    Given a solution of the EFE the equations of motion can then be found using Euler-Lagrange method for the Lagrangian of a body moving in curved space.
    Any textbook on GR has this derivation.
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