There is this general result that for any metric ds2 that is asymptotically AdSd+1, then there is a coordinate system in which
ds2=1r2(dr2+gij(r,xk)dxidxj)
where
gij(r,xk) admit the following expansion close to the (conformal) boundary of
AdSd+1:
gij(r,xk)=g(0)ij(xk)+1rg(1)ij(xk)+O(r−2),
the boundary being at
r→∞ and
1≤i,j,k≤d.
[The above expansion can also contain some rdlog(r) when d is even.]
I now assume that the metric satisfies Einstein's equations with some non-trivial stress-energy tensor.
I guess the radius of convergence of the above series depends on the stress-energy tensor.
My question is: how does the convergence radius depend on the stress-energy tensor?
This post imported from StackExchange Physics at 2014-09-09 10:54 (UCT), posted by SE-user Bru