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 Bañados-Teitelboim-Zanelli 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 Bañados-Teitelboim-Zanelli 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.

• Received 24 February 2013

DOI:https://doi.org/10.1103/PhysRevLett.110.241302