Double layer from least action principle

Abstract

Abstract We derived the equations for the double layers in quadratic gravity, using solely the least action principle. The advantage of our approach is that, in the process of calculation, the δ′-function does not appear at all, and the δ-functions appear for a moment and are mutually canceled prior to integration. We revealed the peculiar structure of the obtained equations, namely, that the surface energy–momentum tensor of the matter fields (constituents of the thin shells) does not play a role in the determination of the trajectory of the double layer. Also, we suggested that the space-like double layers may provide us with the adequate description of the creation of the Universe from the black hole singularity. The related topics, including the Gauss–Bonnet term and F(R)-theories, are shortly discussed.