Thin shell dynamics in Lovelock gravity

TL;DR

This paper derives accurate junction conditions for spherically symmetric thin shells in Lovelock gravity, correcting previous inaccuracies and clarifying the role of boundary terms and canonical momentum in the dynamics.

Contribution

It provides a corrected and systematic derivation of matching conditions for thin shells in Lovelock gravity using boundary terms and canonical momentum analysis.

Findings

Corrected previous results on thin shell collapse in Lovelock theories.

Derived junction conditions based on canonical momentum discontinuity.

Clarified the role of Myers' boundary terms in the variational principle.

Abstract

We study matching conditions for a spherically symmetric thin shell in Lovelock gravity which can be read off from the variation of the corresponding first-order action. In point of fact, the addition of Myers' boundary terms to the gravitational action eliminates the dependence on the acceleration in this functional and such that the canonical momentum appears in the surface term in the variation of the total action. This procedure leads to junction conditions given by the discontinuity of the canonical momentum defined for an evolution normal to the boundary. In particular, we correct existing results in the literature for the thin shell collapse in generic Lovelock theories, which were mistakenly drawn from an inaccurate analysis of the total derivative terms in the system.