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Non-exact solutions in general relativity are
solutions Solution may refer to: * Solution (chemistry), a mixture where one substance is dissolved in another * Solution (equation), in mathematics ** Numerical solution, in numerical analysis, approximate solutions within specified error bounds * Solutio ...
of Albert Einstein's field equations of general relativity which hold only approximately. These solutions are typically found by treating the gravitational field, g, as a background space-time, \gamma, (which is usually an exact solution) plus some small perturbation, h. Then one is able to solve the
Einstein field equations In the General relativity, general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of Matter#In general relativity and cosmology, matter within it. ...
as a
series Series may refer to: People with the name * Caroline Series (born 1951), English mathematician, daughter of George Series * George Series (1920–1995), English physicist Arts, entertainment, and media Music * Series, the ordered sets used i ...
in h, 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 In physics, Minkowski space (or Minkowski spacetime) () is the main mathematical description of spacetime in the absence of general_relativity, gravitation. It combines inertial space and time manifolds into a four-dimensional model. The model ...
, \eta_: ::g_ = \eta_ + h_ +\mathcal(h^2), and dropping all terms which are of second or higher order in h.


See also

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Exact solutions in general relativity In general relativity, an exact solution is a (typically closed form) solution of the Einstein field equations whose derivation does not invoke simplifying approximations of the equations, though the starting point for that derivation may be a ...
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Linearized gravity In the theory of general relativity, linearized gravity is the application of perturbation theory to the metric tensor that describes the geometry of spacetime. As a consequence, linearized gravity is an effective method for modeling the effects ...
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Post-Newtonian expansion In general relativity, post-Newtonian expansions (PN expansions) are used for finding an approximate solution of Einstein field equations for the metric tensor (general relativity), metric tensor. The approximations are expanded in small paramet ...
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Parameterized post-Newtonian formalism In physics, precisely in the study of the theory of general relativity and many alternatives to it, the post-Newtonian formalism is a calculational tool that expresses Einstein's (nonlinear) equations of gravity in terms of the lowest-order de ...
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Numerical relativity Numerical relativity is one of the branches of general relativity that uses numerical methods and algorithms to solve and analyze problems. To this end, supercomputers are often employed to study black holes, gravitational waves, neutron stars a ...


References

General relativity {{Relativity-stub