Linearized field equation

Linearized gravity is an approximation scheme in general relativity in which the nonlinear contributions from the spacetime metric are ignored, simplifying the study of many problems while still producing useful approximate results.

In linearized gravity the metric tensor, ${\displaystyle g}$, of spacetime is treated as a sum of an exact solution of Einstein's equations (often Minkowski spacetime) and a perturbation ${\displaystyle h}$.

where ${\displaystyle \eta }$ is the nondynamical background metric that is being perturbed about, and ${\displaystyle h}$ represents the deviation of the true metric (${\displaystyle g}$) from flat spacetime.

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