“Mass without mass” from thin shells in Gauss-Bonnet gravity

Abstract

Five tensor equations are obtained for a thin shell in Gauss-Bonnet gravity. There is the well-known junction condition for the singular part of the stress tensor intrinsic to the shell, which we also prove to be well defined. There are also equations relating the geometry of the shell (jump and average of the extrinsic curvature as well as the intrinsic curvature) to the nonsingular components of the bulk stress tensor on the sides of the thin shell. The equations are applied to spherically symmetric thin shells in the vacuum. The shells are part of the vacuum; they carry no energy tensor. We classify these solutions of ``thin shells of nothingness'' in the pure Gauss-Bonnet theory. There are three types of solutions, with one, zero, or two asymptotic regions, respectively. The third kind of solutions are wormholes. Although vacuum solutions, they have the appearance of mass in the asymptotic regions. It is striking that in this theory, exotic matter is not needed in order for wormholes to exist---they can exist even with no matter.