Equations · equation
Einstein–Hilbert Action
General Relativity · 1915
- Equation
- S = (c⁴/16πG)·∫R·√(−g)·d⁴x
- Field
- General Relativity
- Named After
- David Hilbert · Albert Einstein
- Year
- 1915
Symbols
R the Ricci scalar, total curvature at each point · g determinant of the metric · the integral runs over all of spacetime · varying S with respect to the metric gives the vacuum field equations; the T_μν side appears only when the matter action is added to it
Significance
All of general relativity compressed into one thing to extremize. Vary it with respect to the metric and the vacuum field equations fall out; add a matter action and its variation is the stress-energy tensor, which is how any new field is coupled to gravity at all — and why the action form is the doorway every attempt at quantum gravity walks through. Hilbert presented a variational route to the theory five days before Einstein's paper of 25 November 1915, and the priority argument that grew out of it outlived both men; his surviving proof sheets, found in 1997, do not contain the explicit field equations, and he credited them to Einstein.
Referenced by
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