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
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).
When the energy-momentum tensor represents a perfect fluid, every Killing vector field preserves the energy density, pressure and the fluid flow vector field.
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