Lightlike singular hypersurfaces in quadratic gravity

TL;DR

This paper derives motion equations for singular hypersurfaces in quadratic gravity, revealing the absence of double layers in Gauss-Bonnet terms and conditions for null hypersurfaces, with applications to conformal gravity.

Contribution

It provides a comprehensive derivation of hypersurface equations in quadratic gravity, clarifies the non-existence of double layers in Gauss-Bonnet terms, and explores null hypersurfaces in conformal gravity.

Findings

No double layers or thin shells in Gauss-Bonnet term.

Null hypersurfaces have no external pressure.

Spherical null hypersurfaces can be double layers under certain conditions.

Abstract

Using the principle of least action, the motion equations for a singular hypersurface of arbitrary type in quadratic gravity are derived. Equations containing the "external pressure" and the "external flow" components of the surface energy-momentum tensor together with the Lichnerowicz conditions serve to find the hypersurface itself, while the remaining ones define arbitrary functions that arise due to the implicit presence of the delta function derivative. It turns out that neither double layers nor thin shells exist for the quadratic Gauss-Bonnet term. It is shown that there is no "external pressure" for null singular hypersurfaces. The Lichnerowicz conditions imply the continuity of the scalar curvature in the case of spherically symmetric null singular hypersurfaces. These hypersurfaces must be thin shells if the Lichnerowicz conditions are necessary. It is shown that for this particular case the Lichnerowicz conditions can be completely removed therefore a spherically symmetric null double layer exists. Spherically symmetric null singular hypersurfaces in conformal gravity are explored as application.