  Galileons are stable null energy condition (NEC) violating perturbations. If
these NEC violating modes are coupled to Einstein gravity, they can cause
violation of the second law of black hole thermodynamics. We demonstrate that
galileons can only be coupled to quadratic gravity since they are generated by
consistent Kaluza-Klein reduction of the Einstein-Hilbert-Gauss-Bonnet action
from 10-dimensions to 4-dimensions. As a result, the NEC violation of galileons
can no longer be the source of the violation of the second law of black hole
thermodynamics.
