Quadratic field equations on the brane

Abstract

It is shown that four dimensional vacuum Einstein solutions simply embedded in five dimensions obey the Gauss-Bonnet-Einstein field equations: $G_{ab}+αGB_{ab}+δ^{55}_{ab}α\exp(-2χ/\sqrtα)GB_4=0$ and the Pauli-Einstein equations $G_{ab}-3αP_{ab}/5=0$, and the Bach-Einstein equations $B_{ab}=0$. General equations are calculated for which these and similar results follow. It is briefly argued that such field equations could be significant on large distance scales.