Can Galileons cause violation of the second law of black hole thermodynamics?

TL;DR

This paper investigates whether galileons, which violate the null energy condition, can lead to violations of black hole thermodynamics, concluding that their coupling constraints prevent such violations.

Contribution

It shows galileons can only couple to quadratic gravity via Kaluza-Klein reduction, preventing NEC violation from violating the second law of black hole thermodynamics.

Findings

Galileons are generated by Kaluza-Klein reduction of Einstein-Hilbert-Gauss-Bonnet action.

Coupling constraints limit galileons to quadratic gravity.

NEC violation by galileons cannot violate the second law of black hole thermodynamics.

Abstract

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.