Double layer from least action principle

TL;DR

This paper derives equations for double layers in Quadratic Gravity using the least action principle, revealing unique structural features and potential cosmological implications, such as universe creation from black hole singularities.

Contribution

It introduces a novel derivation method that avoids delta-prime functions and shows that matter surface energy-momentum does not influence double layer trajectories.

Findings

Derived double layer equations without delta-prime functions.

Found that matter energy-momentum does not affect double layer trajectories.

Suggested space-like double layers could model universe creation from black holes.

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 $\delta'$-function does not appear at all, and the $\delta$-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.