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Expansion in 1/c2
The post-Newtonian approximations are expansions in a small parameter, which is the ratio of the velocity of matter, forming the gravitational field, to the speed of light, which in this case is better called the speed of gravity.
Expansion in h
Another approach is to expand the equations of general relativity in a power series in the deviation of the metric from its value in the absence of gravity
To this end, one must choose a coordinate system in which the eigenvalues of all have absolute values less than 1.
For example, if one goes one step beyond linearized gravity to get the expansion to the second order in h:
Sometimes, as with the Parameterized post-Newtonian formalism, a hybrid approach is used in which both the reciprocal of the speed of gravity and masses are assumed to be small.
- Coordinate conditions
- Einstein–Infeld–Hoffmann equations
- Linearized gravity
- Parameterized post-Newtonian formalism
- Kopeikin, S. (2004). "The speed of gravity in general relativity and theoretical interpretation of the Jovian deflection experiment". Classical and Quantum Gravity 21 (13): 3251–3286.
- Kopeikin, S., Efroimsky, M., Kaplan, G. (2011). Relativistic Celestial Mechanics of the Solar System. Wiley-VCH. p. 860. ISBN 978-3-527-40856-6.
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