  We consider the generalized laws of thermodynamics in massive gravity. Making
use of explicit black hole solutions, we devise black hole merger processes in
which i) total entropy of the system decreases ii) the zero-temperature
extremal black hole is created. Thus, both second and third laws of
thermodynamics are violated. In both cases, the violation can be traced back to
the presence of negative-mass black holes, which, in turn, is related to the
violation of the null energy condition. The violation of the third law of
thermodynamics implies, in particular, that a naked singularity may be created
as a result of the evolution of a singularity-free state. This may signal a
problem in the model, unless the creation of the negative-mass black holes from
positive-mass states can be forbidden dynamically or the naked singularity may
somehow be resolved in a full quantum theory.

General Relativity and Quantum Cosmology;High Energy Physics - Theory