Solvable symmetric black holes in anti-de Sitter spaces

Using symmetric space techniques, we show that closed orbits of Iwasawa subgroups of SO(2,l−1) naturally define the singularity of a black hole causal structure in anti-de Sitter spaces in l≥3l≥3 dimensions. In particular, we recover for l=3l=3 the non-rotating massive BTZ black hole. The method presented here is very simple and in principle generalizable to any semi-simple symmetric space.