So Einstein Equation: ##G_{uv}= 8 \pi G T_{uv} ##,(adsbygoogle = window.adsbygoogle || []).push({});

Justifying the cosmological constant can be included is done by noting that ## \bigtriangledown^{a}g_{ab} =0 ## and so including it on the LHS, conservation of energy-momentum tensor still holds.

I'm not sure why ## \bigtriangledown^{a}g_{ab} =0 ##. The source I'm using says to 'recall' this, and it is talking about the FRW tensor.

The only thing I can think of is the fundamental theorem of Riemannian geometry : ## \bigtriangledown_{a}g_{bc}= 0 ##. But this doesn't does look right as it has 3 free indicies, not 1, and a lower indice instead of a upper on the ## \bigtriangledown ##

Thanks for your help in advance.

On a side note, I think I am confused between 'divergence' and 'covariant derivative', when we say ## \bigtriangledown_{a} T^{ab} = 0 ##, conservation of energy-momentum tensor that its 'divergence' is zero, is this saying it's convariant derivative is zero?

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

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

# Cosmological Constant, Einstein equation Quick Question

Loading...

Similar Threads - Cosmological Constant Einstein | Date |
---|---|

I Metric for the Lambdavacuum | Aug 26, 2017 |

A Cosmological constant in the semiclassical limit of quantum gravity | Jun 17, 2017 |

Relationship Between Spatial Expansion and Gravity's Force? | Dec 29, 2015 |

Einstein tensor with the cosmological constant present. | Dec 3, 2012 |

Question about Einstein inserting the cosmological constant | Aug 25, 2012 |

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