Junction conditions for F(R)-gravity and their consequences

TL;DR

This paper derives the junction conditions for F(R) gravity theories, revealing stricter matching criteria than in General Relativity and uncovering unique properties in quadratic F(R) models, with implications for modeling astrophysical objects.

Contribution

It provides the generalized junction conditions for F(R) gravity, including new results for quadratic models and their effects on matching solutions and shell properties.

Findings

Junction conditions in F(R) gravity are stricter than in GR.

Quadratic F(R) models can have discontinuous R with unique shell properties.

Matched solutions in GR generally do not satisfy F(R) models.

Abstract

I present the junction conditions for F(R) theories of gravity and their implications: the generalized Israel conditions and equations. These junction conditions are necessary to construct global models of stars, galaxies, etc., where a vacuum region surrounds a finite body in equilibrium, as well as to describe shells of matter and braneworlds, and they are stricter than in General Relativity in both cases. For the latter case, I obtain the field equations for the energy-momentum tensor on the shell/brane, and they turn out to be, remarkably, the same as in General Relativity. An exceptional case for quadratic F(R), previously overlooked in the literature, is shown to arise allowing for a discontinuous R, and leading to an energy-momentum content on the shell with unexpected properties, such as non-vanishing components normal to the shell and a new term resembling classical dipole distributions. For the former case, they do not only require the agreement of the first and second fundamental forms on both sides of the matching hypersurface, but also that the scalar curvature R and its first derivative agree there too. I argue that, as a consequence, matched solutions in General Relativity are not solutions of F(R)-models generically. Several relevant examples are analyzed.