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

Say that one can separate the metric of a space time in a background metric and a small perturbation such that [itex]g_{\alpha \beta}=g'_{\alpha \beta}+h_{\alpha \beta}[/itex], where [itex]g'_{\alpha \beta}[/itex] is the background metric and [itex]h_{\alpha \beta}[/itex] the perturbation.

Computing the christoffel symbols one would get, to first order in the perturbation: [tex]\Gamma^\alpha_{\beta \gamma}=\Gamma'^\alpha_{\beta \gamma}+\frac{1}{2}(h^{\alpha}_{\beta,\gamma}+h^{ \alpha }_{\gamma,\beta}-h_{\beta \gamma}\hspace{.2mm}^{,\alpha}),[/tex]

right?

Then why, in this reference, in the text right after Eq.19.23, [itex]C^\alpha_{\beta \gamma}=\frac{1}{2}(h^{\alpha}_{\beta;\gamma}+h^{ \alpha }_{\gamma;\beta}-h_{\beta \gamma}\hspace{.2mm}^{;\alpha})[/itex], is written with covariant derivatives?

Thank you

**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!

# Linearized Einstein Field Equations

Loading...

Similar Threads - Linearized Einstein Field | Date |
---|---|

A Multipole expansion of linearized field equations | May 16, 2017 |

B Linear momentum | Jan 23, 2017 |

I Help with derivation of linearized Einstein field equations | Oct 25, 2016 |

A Linearized metric for GW emitting orbiting bodies | Jul 26, 2016 |

Linearized gravity / Linearized Einstein Field Equations / GEM | Dec 1, 2007 |

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