Scalar-tensor gravity and conformal continuations

Abstract

Global properties of vacuum static, spherically symmetric configurations are studied in a general class of scalar-tensor theories (STT) of gravity in various dimensions. The conformal mapping between the Jordan and Einstein frames is used as a tool. Necessary and sufficient conditions are found for the existence of solutions admitting a conformal continuation (CC). The latter means that a singularity in the Einstein-frame manifold maps to a regular surface S_(trans) in the Jordan frame, and the solution is then continued beyond this surface. S_(trans) can be an ordinary regular sphere or a horizon. In the second case, S_(trans) proves to connect two epochs of a Kantowski-Sachs type cosmology. It is shown that, in an arbitrary STT, with arbitrary potential functions $U(ϕ)$, the list of possible types of causal structures of vacuum space-times is the same as in general relativity with a cosmological constant. This is true even for conformally continued solutions. It is found that when S_(trans) is an ordinary sphere, one of the generic structures appearing as a result of CC is a traversable wormhole. Two explicit examples are presented: a known solution illustrating the emergence of singularities and wormholes, and a nonsingular 3-dimensional model with an infinite sequence of CCs.