Junction conditions and sharp gradients in generalized coupling theories

TL;DR

This paper develops a formalism for analyzing sharp matter density gradients in generalized coupling theories, showing they avoid typical pathologies and can influence gravitational collapse dynamics.

Contribution

It introduces a variational formalism for junction conditions in generalized coupling theories and applies it to demonstrate the stability of sharp density gradients.

Findings

Sharp gradients do not cause singularities in these theories.

An auxiliary field does not lead to pathologies at boundaries.

Additional forces affect matter distribution during collapse.

Abstract

In this article, we develop the formalism for singular hypersurfaces and junction conditions in generalized coupling theories using a variational approach. We then employ this formalism to examine the behavior of sharp matter density gradients in generalized coupling theories. We find that such gradients do not necessarily lead to the pathologies present in other theories of gravity with auxiliary fields. A detailed example, based on a simple instance of a generalized coupling theory called the MEMe model, is also provided. In the static case, we show that sharp boundaries do not generate singularities in the dynamical frame despite the presence of an auxiliary field. Instead, in the case of a collapsing spherical density distribution with a general profile an additional force compresses over-densities and expands underdensities. These results can also be used to deduce additional constraints on the parameter of this model.