Generalized Gibbons-Hawking-York term for f(R) gravity

Abstract

A derivation of the Gibbons-Hawking-York boundary term for modified gravity metric is presented. The GHY term is generalized for the case of f(R) modified gravity. It is shown that a stable set of field equations can be formed with aid of the new GHY term for the case of f(R) gravity action. It is proven that the new term demands no particular value of δga or ∂Lδga on the boundary. Finally, the surface terms are shown to vanish in the derivation of the new equations.