Massless limit to massive scalar in AdS space

Question

I was trying to solve massive scalar wave equation in AdS spacetime (or rather in BTZ). I noticed few funny things :

1. The $m\to 0$ limit to the solution is subtle. One of the two independent solutions diverges! But the other one solves the massless wave equation. Is it very generic case? The possible reason I have in mind is following. The massless scalar action enjoys more symmetry namely $\phi \to \phi+ const$ which the massive one does not. May be this enhanced global symmetry plays a role.. but I am not sure.

2. The other thing is I tried to solve the $massless$ wave equation in BTZ background using mathematica. It couldn't solve it. But the massive one is solved very fast. This might be a technical part though, but I am a bit surprised.

This post imported from StackExchange Physics at 2015-09-21 17:23 (UTC), posted by SE-user pinu