I'm currently working through General Relativity and I'm wondering how you would express the variation of a general metric tensor, or similarly, how you would write the total differential of a metric tensor (analogous to how you would write the total derivative for a function)? Also, on a related note, does the covariant derivative of the metric always vanish, regardless of the metric chosen?(adsbygoogle = window.adsbygoogle || []).push({});

**Physics Forums | Science Articles, Homework Help, Discussion**

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

# Variation of the metric tensor

**Physics Forums | Science Articles, Homework Help, Discussion**