Post-Newtonian expansion

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Post-Newtonian expansions in general relativity are used for finding an approximate solution of the Einstein equations for the metric tensor that represents a multi-component, tensor gravitational field potential instead of a single, scalar gravitational potential in the Newtonian gravity. The post-Newtonian approximations are done with respect to a small parameter of the theory which is the ratio of the velocity of matter, forming the gravitational field, to the fundamental speed of gravity.

In the limit, when the fundamental speed of gravity approaches to infinity, the post-Newtonian expansions degenerate and the Einstein theory of general relativity is reduced to the Newtonian-like theory of gravity with the instantaneous action-at-the-distance gravitational field interaction.

Sometimes, the fundamental speed of gravity in general relativity is misleadingly called as the speed of light. This jargon is well-spread among physics community and stems from the language adopted in electrodynamics where the parameter of the linear Lorentz transformation of electromagnetic field is associated with the speed of light in vacuum. The Lorentz transformation of gravitational field is parametrized by the fundamantal speed of gravity which is not associated with the speed of electromagnetic field but must be numerically equal to this speed if general relativity is correct.