Exact anyon black hole solutions

We present the exact anyon solutions and study their energy conditions. It is shown that the exact anyon VdW solutions with \(b>0\) are physically un-acceptable. Especially for the reduced case \(b=0\), after carefully studying its energy conditions, geometric quantities and horizon structure, we conclude that there is an anyon black hole taking the precisely same thermodynamical phase space with the gas of “interacting point particle” (IPP), which should exhibit a quasi Fermi–Dirac statistics and have an upper bound of mass. The anyon IPP black hole can contain 1 or 2 horizons. This is the first physical VdW-like black hole solution in the global spacetime. Moreover, there exist the Hawking-Page phase transition between the anyon IPP black holes and the pure thermal radiation phase.