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

TL;DR

This paper generalizes boundary terms for quadratic gravity theories, derives junction conditions including Gauss-Bonnet gravity, and compares these with existing results, enhancing understanding of boundary conditions in higher-order gravity.

Contribution

It introduces a simple condition to obtain Gibbons-Hawking-York boundary terms for quadratic gravity theories and derives corresponding junction conditions, including for Gauss-Bonnet gravity.

Findings

Derived junction conditions for quadratic gravity theories.

Re-obtained known results for Gauss-Bonnet gravity.

Compared new junction conditions with existing literature.

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 re-obtain 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