P-matrix

Non-exact solutions in general relativity are solutions 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 as a series 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, ${\eta }_{\mu \nu }$:

$g_{\mu \nu }={\eta }_{\mu \nu }+h_{\mu \nu }+\mathcal{𝒪}(h^2)$,

and dropping all terms which are of second or higher order in $h$.

See also

• Exact solutions in general relativity
• Linearized gravity
• Post-Newtonian expansion
• Parameterized post-Newtonian formalism
• Numerical relativity

References

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