The fate of black hole thermodynamics under Weyl transformations is investigated by going back to the laws of black hole mechanics. It is shown that the transformed surface gravity, that one would identify with the black hole temperature in the conformal frame, as well as the black hole entropy, that one would identify with the horizon area, cannot be invariant. It is also shown that the conformally invariant surface gravity, attributed to the so-called "conformal Killing horizon", cannot represent the black hole temperature in the conformal frame. Finally, using familiar thought experiments, we find that the effect a Weyl transformation should have on black hole thermodynamics becomes even subtler than what is suggested by the laws of black hole mechanics.

We show that the violation of the null energy condition by matter, required by traversable wormholes, can be removed in spacetimes with torsion. In addition, we show that this violation can also be removed in the conformal frame obtained by a Weyl transformation. This comes about because both conformally transformed wormholes and wormholes in spacetimes with torsion become sustained thanks to a combination of "normal" matter, that satisfies the null energy condition, and an induced "geometric" energy-momentum tensor that is able to greatly violate the null energy condition.PACS numbers: 04.50.Kd, 04.90.+e, 02.40.Ky * fhammad@ubishops.ca † Etienne.Masse@usherbrooke.ca ‡ plabelle@crc-lennox.qc.ca 1 Throughout the paper, we set 8πG = = c = 1.