Say I have a vector field $\displaystyle k^{\mu}$defined on a space such as $\displaystyle R^{2,p}$ Actually, it is AdS space im working on but I don't think that matters for what I want to ask. I assume that I can write the coordinates as (time,radial, p-angles)

Now if I take the integral of the divergence of the field

$\displaystyle \int \partial_{\mu}k^{\mu}dx^{p+2}$ then by the divergence theorem this gives zero if K dies of sufficiently quickly at spatial (and temporal)infinity i.e. (r --->infinity)

Everything works as I want it to if I take it to die of as 1/r or quicker. Unless I have made a mistake, then any other possibility doesn't work like I think it should.

Can any one reassure me about this.