  An exotic Banados-Teitelboim-Zanelli (BTZ) black hole has an angular momentum
larger than its mass in three dimension (3D), which suggests the possibility
that cosmic censorship could be violated if angular momentum is extracted by
the Penrose process. In this paper, we propose a mass formula for the exotic
BTZ black hole and show no violation of weak cosmic censorship in the gedanken
process above by understanding properly its mass formula. Unlike the other
black holes, the total energy of the exotic BTZ black hole is represented by
the angular momentum instead of the mass, which supports a basic point of view
that the same geometry should be determined by the same energy in 3D general
relativity whose equation of motion can be given either by normal 3D Einstein
gravity or by exotic 3D Einstein gravity. However, only the mass of the exotic
black hole is related to the thermodynamics and other forms of energy are
"dumb", which is consistent with the earlier thermodynamic analysis about
exotic black holes.
