  A number of three-dimensional (3D) gravity models, such as 3D conformal
gravity, admit "exotic" black hole solutions: the metric is the same as the BTZ
metric of 3D Einstein gravity but with reversed roles for mass and angular
momentum, and an entropy proportional to the length of the inner horizon
instead of the event horizon. Here we show that the BTZ solutions of the
"exotic" 3D Einstein gravity (with parity-odd action but Einstein field
equations) are exotic black holes, and we investigate their thermodynamics. The
first and second laws of black hole thermodynamics still apply, and the entropy
still has a statistical interpretation.
