What are the effects of higher derivatives in the slow-motion approach?

[eljose]

Hello i didn,t understand the slow motion approach of course i know that:

$$\frac{\partial f }{\partial x^{0}}\sim \epsilon \frac{\partial f }{\partial x^{a}}$$ according to this approach with epsilon<<<1 small parameter for every smooth function my doubts are.

a)what would happen to higher derivatives of f with respect to time and spatial coordinates?..x,y,z ?

b)If we only want effect upto first order in epsilon parameter then..what would happen to:

$$\nabla ^{2}f$$ (Laplacian)

$$(1,1,1)*Gra(f)$$ (scalar product involving the gradient)

or if we had $$\epsilon div(f)$$ would it mean that the only term that should be kept is df/dt if we consider effects only to first order?..

thanks.

 

[pervect]

I've been trying to fill in the context of this post, with little success. Regarding what problem are you taking a "slow motion" approach? Are you doing low-velocity, weak-field approximations to GR?