Quasi-Poisson actions and massive non-rotating BTZ black holes

Using ideas from an article of Bieliavsky, Rooman and Spindel on BTZ black holes, I construct a family of interesting examples of quasi-Poisson actions as defined by Alekseev and Kosmann-Schwarzbach. As an application, I obtain a genuine Poisson structure on SL(2,R) which induces a Poisson structure on a BTZ black hole.