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A matter collineation (sometimes matter symmetry and abbreviated to MC) is a vector field that satisfies the condition, : where are the energy-momentum tensor components. The intimate relation between geometry and physics may be highlighted here, as the vector field is regarded as preserving certain physical quantities along the flow lines of , this being true for any two observers. In connection with this, it may be shown that ''every Killing vector field is a matter collineation'' (by the Einstein field equations (EFE), with or without cosmological constant). Thus, given a solution of the EFE, ''a vector field that preserves the metric necessarily preserves the corresponding energy-momentum tensor''. When the energy-momentum tensor represents a perfect fluid, every Killing vector field preserves the energy density, pressure and the fluid flow vector field. When the energy-momentum tensor represents an electromagnetic field, a Killing vector field does ''not necessarily'' preserve the electric and magnetic fields. ==See also== * Affine vector field * Conformal vector field * Curvature collineation * Homothetic vector field * Spacetime symmetries 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Matter collineation」の詳細全文を読む スポンサード リンク
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