- #1

- 15

- 0

## Main Question or Discussion Point

In the weak field approximation,

[itex]g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}[/itex]

If we make a coordinate transformation of the form

[itex]x^{\mu'}=x^{\mu}+\xi^{\mu}(x)[\itex]

it changes [itex]h_{\mu\nu}[\itex] to

[itex]h'_{\mu\nu}=h_{\mu\nu}+\xi_{\mu,\nu}+\xi_{\nu,\mu}+O(\xi^{2})[\itex]

I was wondering if anyone could shed some light on what form the higher order terms take. I have an inkling it's terms from a taylor series expansion but i'm not sure.

Thanks

[itex]g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}[/itex]

If we make a coordinate transformation of the form

[itex]x^{\mu'}=x^{\mu}+\xi^{\mu}(x)[\itex]

it changes [itex]h_{\mu\nu}[\itex] to

[itex]h'_{\mu\nu}=h_{\mu\nu}+\xi_{\mu,\nu}+\xi_{\nu,\mu}+O(\xi^{2})[\itex]

I was wondering if anyone could shed some light on what form the higher order terms take. I have an inkling it's terms from a taylor series expansion but i'm not sure.

Thanks