View source for Non-exact solutions in general relativity

'''Non-exact solutions in general relativity''' are [[Solutions of the Einstein field equations|solutions]] of Albert Einstein's [[Einstein field equations|field equations of general relativity]] which hold only approximately. These solutions are typically found by treating the gravitational field, <math>g</math>, as a background space-time, <math>\gamma</math>, (which is usually an exact solution) plus some small perturbation, <math>h</math>. Then one is able to solve the [[Einstein field equations]] as a [[Power series solution of differential equations|series]] in <math>h</math>, dropping higher order terms for simplicity.

A common example of this method results in the [[linearised Einstein field equations]].  In this case we expand the full space-time metric about the flat [[Minkowski metric]], <math>\eta_{\mu\nu}</math>:

::<math>g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu} +\mathcal{O}(h^2)</math>,

and dropping all terms which are of second or higher order in <math>h</math>.<ref name="Carroll2004">{{cite book|author=Sean M. Carroll|title=Spacetime and Geometry: An Introduction to General Relativity|url=https://books.google.com/books?id=1SKFQgAACAAJ|year=2004|publisher=Addison-Wesley Longman, Incorporated|isbn=978-0-8053-8732-2|pages=274–279}}</ref>

==See also==
* [[Exact solutions in general relativity]]
* [[Linearized gravity]]
* [[Post-Newtonian expansion]]
* [[Parameterized post-Newtonian formalism]]
* [[Numerical relativity]]

==References==

{{Reflist}}

{{DEFAULTSORT:Non-Exact Solutions In General Relativity}}
[[Category:General relativity]]


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