Lightlike singular hypersurfaces in quadratic gravity

For a singular hypersurface of arbitrary type in quadratic gravity equations of motion were obtained using the principle of least action. The equations containing the components of the surface energy-momentum tensor corresponding to the “external pressure” and “external flow” together with the Lichnerowicz conditions are necessary to find the hypersurface itself, while the rest of the equations define “arbitrary” functions that arise due to the implicit presence of derivative of the delta function. It turned out that there are no double layers or thin shells for the Gauss-Bonnet quadratic term. It was demonstrated that there is no “external pressure” for null singular hypersurfaces. For spherically symmetric lightlike singular hypersurfaces the “external flux” is additionally equal to zero; therefore, such hypersurfaces can only be thin shells. In this case the system of equations of motion is reduced to one, which is expressed through the invariants of spherical geometry along with the Lichnerowicz conditions.