On page 161 of Carroll's(adsbygoogle = window.adsbygoogle || []).push({}); Spacetime and Geometry, Carroll writes that

[tex]\delta g_{\mu\nu}=-g_{\mu\rho}g_{\nu\sigma}\delta g^{\rho\sigma}.[/tex]

##\delta g_{\alpha \beta}## denotes an arbitrary, infinitesimal variation of the metric.

Why is there a minus sign? By the regular rules of raising and lowering indices, shouldn't it just be

[tex]\delta g_{\mu\nu}=g_{\mu\rho}g_{\nu\sigma}\delta g^{\rho\sigma}?[/tex]

**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!

# Error in Carroll?

Loading...

Similar Threads - Error Carroll | Date |
---|---|

A Sean Carroll Notes, Schwarzschild derivation, theorem name? | Mar 5, 2018 |

B Error about the twin paradox in Einstein's biography? | May 18, 2017 |

I Lorentz invariant integration - where is the error? | Mar 2, 2017 |

I Complex number 'isomorphism' error | Nov 20, 2016 |

B Error in laws of motion | Apr 10, 2016 |

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