Editing Classical field theory (section)

=== Gravitation ===
{{Main|Gravitation}}
{{Further|General Relativity|Einstein field equation}}

After Newtonian gravitation was found to be inconsistent with [[special relativity]], [[Albert Einstein]] formulated a new theory of gravitation called [[general relativity]]. This treats [[gravitation]] as a geometric phenomenon ('curved [[spacetime]]') caused by masses and represents the [[gravitational field]] mathematically by a [[tensor field]] called the [[metric tensor (general relativity)|metric tensor]]. The [[Einstein field equations]] describe how this curvature is produced. [[Newtonian gravitation]] is now superseded by Einstein's theory of [[general relativity]], in which [[gravitation]] is thought of as being due to a curved [[spacetime]], caused by masses. The Einstein field equations,
<math display="block">G_{ab} = \kappa T_{ab} </math>
describe how this curvature is produced by matter and radiation, where ''G<sub>ab</sub>'' is the [[Einstein tensor]],
<math display="block">G_{ab} \, = R_{ab}-\frac{1}{2} R g_{ab}</math>
written in terms of the [[Ricci tensor]] ''R<sub>ab</sub>'' and [[Ricci scalar]] {{math|1=''R'' = ''R<sub>ab</sub>g<sup>ab</sup>''}}, {{math|''T<sub>ab</sub>''}} is the [[stress–energy tensor]] and {{math|1=''κ'' = 8''πG''/''c''<sup>4</sup>}} is a constant. In the absence of matter and radiation (including sources) the '[[vacuum field equations]]'',
<math display="block">G_{ab} = 0 </math>
can be derived by varying the [[Einstein–Hilbert action]],
<math display="block"> S = \int R \sqrt{-g} \, d^4x </math>
with respect to the metric, where ''g'' is the [[determinant]] of the [[metric tensor (general relativity)|metric tensor]] ''g<sup>ab</sup>''. Solutions of the vacuum field equations are called [[vacuum solution]]s. An alternative interpretation, due to [[Arthur Eddington]], is that <math>R</math> is fundamental, <math>T</math> is merely one aspect of <math>R</math>, and <math>\kappa</math> is forced by the choice of units.