Junction conditions for higher order gravity theories from a Gibbons-Hawking-York boundary term

Abstract

In this work, we study the problem of generalizing the Gibbons-Hawking-York boundary terms for general quadratic theories of gravity and propose a simple condition to obtain them. From these terms, we derive the junction conditions for a subset of this family of theories that includes Gauss-Bonnet (GB) gravity. We reobtain the well-known results for GB theory, generalize them to other quadratic theories, and compare the resulting junction conditions with the ones already derived in the literature using other methods.