Lovelock's theorem of general relativity says that from a local gravitational action which contains only second derivatives of the four-dimensional spacetime metric, then the only possible equations of motion are the Einstein field equations.
[1][2][3] The theorem was described by British physicist David Lovelock in 1971.
In four dimensional spacetime, any tensor
whose components are functions of the metric tensor
), and also symmetric and divergence-free, is necessarily of the form where
[3] The only possible second-order Euler–Lagrange expression obtainable in a four-dimensional space from a scalar density of the form
Lovelock's theorem means that if we want to modify the Einstein field equations, then we have five options.
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