Why does a perturbed geodesic obey the geodesic equation?

[Isa1]

Hi there,

I'm trying to understand the derivation of geodesic deviation given here:

http://wps.aw.com/wps/media/objects/500/512494/supplements/Ch21.pdf

but I can't figure out why x(t)+\chi(t) obeys the geodesic equation (eq.(7)). Of course x(t) does, since it is per definition a geodesic. Could it be that \chi(t) is so small that it is negligible and doesn't change the geodesic character of x(t)?

I'd really appreciate some help. Thanks!

 

[Altabeh]

Hi there,

I'm trying to understand the derivation of geodesic deviation given here:

http://wps.aw.com/wps/media/objects/500/512494/supplements/Ch21.pdf

but I can't figure out why x(t)+\chi(t) obeys the geodesic equation (eq.(7)). Of course x(t) does, since it is per definition a geodesic. Could it be that \chi(t) is so small that it is negligible and doesn't change the geodesic character of x(t)?

I'd really appreciate some help. Thanks!

It is because the point $$x(\tau)+\chi(\tau)$$ is in the beginning of the paper said to be on a nearby geodesic at the same proper time so no matter if $$\chi(\tau)$$ is small!

AB