to remove perturbative dynamical instabilities. Nevertheless, one still worries about the second law of thermodynamics, particularly as generalized to include the entropy of black holes. To see the point, consider a process in which a bit of a negative tension brane is lowered into a black hole (or, equivalently, in which a black hole is thrown at a negative tension brane). Heuristically, one expects that as negative energy matter flows into the black hole, the black hole will shrink and reduce in entropy. In the semi-classical limit, the entropy of a black hole should dominate over all other forms of entropy and one expects a reduction in black hole area to lead to a violation of the generalized second law of thermodynamics.

In [@NegT], exact constructions were given of spacetimes representing collisions in 2+1 dimensional gravity between BTZ black holes and 1+1 dimensional negative tension branes at orbifolds. The results are interesting in that one can prove that if the system were to settle down to some equilibrium state representing a black hole attached to the brane, then a violation of the second law would necessarily result. However, in this case such clear violations are avoided by the onset of 