Is there a simple geometric interpretation of the Einstein tensor ? I know about its algebraic definitions ( i.e. via contraction of Riemann's double dual, as a combination of Ricci tensor and Ricci scalar etc etc ), but I am finding it hard to actually understand it geometrically.(adsbygoogle = window.adsbygoogle || []).push({});

Specifically, what I am looking for is an interpretation along the lines of what Misner/Thorne/Wheeler do in "Gravitation" for the Riemann tensor, in terms of the "slots" of tensor understood as being a linear "machine". You take the tangent vector to a reference geodesic, insert it into both slots 1 and 3 of Riemann, and insert the separation vector to some neighbouring geodesic into slot 2; the result is a vector which signifies the ( covariant ) rate of change of your separation vector ( relative acceleration ) between the geodesics, with respect to your chosen time coordinate. Geodesic deviation, in other words.

Can something similar be done with the Einstein tensor ?

Apologies in advance if this question turns out to be either meaningless, imprecise, or trivial. Hopefully you can see what I am trying to get at.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Geometric Interpretation of Einstein Tensor

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - Geometric Interpretation Einstein | Date |
---|---|

Geodesics by Plane Intersection | Jan 3, 2016 |

Question on Phenomena beyond General Relativity | Dec 20, 2015 |

Geometric interpretation of the spacetime invariant | Oct 17, 2010 |

Help with geometric interpretation of 1-form | Feb 8, 2010 |

Torsion tensor: Geometric interpretation | Mar 29, 2007 |

**Physics Forums - The Fusion of Science and Community**