Hi(adsbygoogle = window.adsbygoogle || []).push({});

Can anyone explain why from varying a Lagrangian?

[itex] \frac{\partial \mathcal{L}}{\partial (\partial_{\alpha }\phi)}(\frac{1}{2}\sqrt{-g}g^{\alpha\beta}\partial_{\alpha} \phi \partial_{\beta} \phi) = g^{\mu\nu}\partial_{\mu}\partial_{\nu}\phi + \frac{1}{\sqrt{-g}}(\partial_{\nu}\phi)\partial_{\mu}(g^{\alpha \beta}\sqrt{-g}) [/itex]

I realise that the indices are dummies and so can be renamed accordingly but I don't understand why it isn't equal to:

[itex] (\frac{1}{2}g^{\mu\nu} \partial_{\nu} \phi) + \frac{1}{\sqrt{-g}}(\partial_{\mu} \phi) \partial_{\mu}(\frac{1}{2}\sqrt{-g}g^{\mu\nu} \partial_{\nu} \phi)

[/itex]

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

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

# Variational principles within GR

Loading...

Similar Threads for Variational principles within |
---|

I Issues with the variation of Christoffel symbols |

I Consequence of a variation of c in rest mass |

A Variation of scalar field action |

A Derive the Bianchi identities from a variational principle? |

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