This question is motivated by the results in this paper, http://calvino.polito.it/~camporesi/JMP94.pdf
In this paper some of its most important results about the asymptotics of symmetric traceless transverse harmonic ranks tensors on $\mathbb{H}_n = EAdS_n$ in equations 2.27, 2.28, 2.88, 2.89 are all given in hyperbolic coordinates.
But for reasons of physics one wants to write $\mathbb{H}_n$ in the Poincare patch!
How does one convert between the two? Is there a known transformation?

I would like to know if the largey (variable defined below) behaviour as stated in the said equations of the linked paper can be converted to find the smallz behaviour (variable defined below)

Or is there a reference where these results have already been found in terms of the Poincare patch coordinates?
 In the hyperbolic model of $\mathbb{H}_n$ the space is thought of a zeroset in $\mathbb{R}^{n+1}$ of the equation, $x_0^2  \sum_{i=1}^n x_i ^2 = a^2$ and then one uses the coordinates $y \in [0,\infty)$ and and $\vec{n} \in S^{n1}$ to write, $x_0 = a \cosh y$ and $\vec{x} = a \vec{n} \sinh y$ and then the metric is, $ds^2 = a^2 [ dy^2 + \sinh ^ 2 yd\Omega_{n1}^2]$
Here $d\Omega_{n1}^2$ is the standard metric on $S^{n1}$.
(..and this is the metric in equation 2.15 in the linked paper..)
 In the Poincare patch model of $\mathbb{H}_n$ it is thought of as the halfspace $x_n > 0$ in $\mathbb{R}^n$ with the metric, $ds^2 = \frac{a^2}{z^2}(dz^2 + \sum_{i=1}^{n1}dx_i^2 )$
(relabeling $x_n$ as $z$)
This post imported from StackExchange MathOverflow at 20140909 10:51 (UCT), posted by SEuser user6818