Post-Newtonian approximation in Maxwell-like form - APS Link 2025

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The metric equation in special relativity, as it is often written, has two times and one displacement in it, e.g. (c dT)^2 = (c dt)^2 - (dx)^2 where c is the speed of light.
The post-Newtonian approximation is valid under the assumptions of a weak gravitational field inside the source, and of slow internal motions. When assuming a source is post-Newtonian, it mainly means that the source is at once slowly moving and weakly stressed.
In physics, precisely in the general theory of relativity, post-Minkowskian expansions (PM) or post-Minkowskian approximations are mathematical methods used to find approximate solutions of Einsteins equations by means of a power series development of the metric tensor.
In essence, the Minkowski force is the rate of change of the momentum four-vector with respect to proper time, which is the time measured by an observer moving with the object in question. This is expressed mathematically as F = d P d , where is the momentum four-vector and represents proper time.
Minkowski space or spacetime is used in mathematical physics and special relativity. It combines 3-dimensional Euclidean Space and time into a 4-dimensional manifold, where the interval of spacetime that exists between any two events is not dependent on the inertial frame of reference.
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The post-Newtonian approximation is a method for solving Einsteins field equations for physical systems in which motions are slow compared to the speed of light and where gravitational fields are weak.

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