The fate of black holes in an accelerating universe

Babichev, Dokuchaev and Eroshenko have recently found that accretion of phantom energy onto a black hole induces a gradual decrease of the black hole mass, and that masses of all possible black holes tend to zero as a result of this process as the universe approaches the big rip singularity. The implications of these results on the thermodynamics of black holes and phantom energy are explored in this Letter, showing that such results become consistent with the two first laws of thermodynamics only if phantom energy is characterized by a negative temperature depending on the scale factor and by a positive definite entropy which tends to become constant if phantom energy largely dominates the universe. It is also argued that the loss of quantum coherence of semiclassical black hole physics is no longer present if the universe is filled with phantom energy. (C) 2004 Elsevier B.V. All rights reserved.